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Annual Review of Fluid Mechanics top

► Space-Time Correlations and Dynamic Coupling in Turbulent Flows
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 51-70, January 2017.
► Combustion and Engine-Core Noise
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 277-310, January 2017.
► Uncertainty Quantification in Aeroelasticity
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 361-386, January 2017.
► Simulation Methods for Particulate Flows and Concentrated Suspensions
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 171-193, January 2017.
► Model Reduction for Flow Analysis and Control
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 387-417, January 2017.
► Vapor Bubbles
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 221-248, January 2017.
► Saph and Schoder and the Friction Law of Blasius
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 575-582, January 2017.
► Recent Developments in the Fluid Dynamics of Tropical Cyclones
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 541-574, January 2017.
► Inflow Turbulence Generation Methods
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 23-49, January 2017.
► Blood Flow in the Microcirculation
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 443-461, January 2017.

Computers & Fluids top

► A low-dissipation convection scheme for the stable discretization of turbulent interfacial flow
  25 Jun, 2017
Publication date: 10 August 2017
Source:Computers & Fluids, Volume 153
Author(s): Eugenio Schillaci, Lluís Jofre, Néstor Balcázar, Oscar Antepara, Assensi Oliva
This paper analyzes a low-dissipation discretization for the resolution of immiscible, incompressible multiphase flow by means of interface-capturing schemes. The discretization is built on a three-dimensional, unstructured finite-volume framework and aims at minimizing the differences in kinetic energy preservation with respect to the continuous governing equations. This property plays a fundamental role in the case of flows presenting significant levels of turbulence. At the same time, the hybrid form of the convective operator proposed in this work incorporates localized low-dispersion characteristics to limit the growth of spurious flow solutions. The low-dissipation discrete framework is presented in detail and, in order to expose the advantages with respect to commonly used methodologies, its conservation properties and accuracy are extensively studied, both theoretically and numerically. Numerical tests are performed by considering a three-dimensional vortex, an exact sinusoidal function, and a spherical drop subjected to surface tension forces in equilibrium and immersed in a swirling velocity field. Finally, the turbulent atomization of a liquid-gas jet is numerically analyzed to further assess the capabilities of the method.

► Erratum to: “Volume of Fluid (VOF) type advection methods in two-phase flow: A comparative study”. [Comput Fluids 97 (2014) 52–73]
  25 Jun, 2017
Publication date: 18 July 2017
Source:Computers & Fluids, Volume 152
Author(s): W. Aniszewski, T. Ménard, M. Marek


► The simulation of compressible multi-fluid multi-solid interactions using the modified ghost method
  25 Jun, 2017
Publication date: 1 September 2017
Source:Computers & Fluids, Volume 154
Author(s): Z.W. Feng, A. Kaboudian, J.L. Rong, B.C. Khoo
Based on the Modified Ghost Fluid Method (MGFM) and Modified Ghost Solid Method (MGSM), the Modified Ghost Method (MGM) is developed to deal with the combined compressible multi-fluid multi-solid interactions. The exact solution for 1D fluid-elastic-plastic solid Riemann problem is derived, which is subsequently used to verify the validity of the MGM as applied to fluid-elastic-plastic solid interaction. Using MGM, we construct a coherent and consistent approach to simulate truly compressible multi-medium problems as for gas-water-solid-solid interaction. Similar to the 1D cases, several 2D multi-medium cases are simulated to show the versatility and ease of application for the MGM. Finally, a multi-medium case with a complex geometry in solid domain is simulated, which shows that the proposed approach can be effectively used to study the response of the various structure domain.

► An immersed boundary-based large-eddy simulation approach to predict the performance of vertical axis tidal turbines
  25 Jun, 2017
Publication date: 18 July 2017
Source:Computers & Fluids, Volume 152
Author(s): Pablo Ouro, Thorsten Stoesser
Vertical axis tidal turbines (VATTs) are perceived to be an attractive alternative to their horizontal axis counterparts in tidal streams due to their omni-directionality. The accurate prediction of VATTs demands a turbulence simulation approach that is able to predict accurately flow separation and vortex shedding and a numerical method that can cope with moving boundaries. Thus, in this study an immersed boundary-based large-eddy simulation (LES-IB) method is refined to allow accurate simulation of the blade vortex interaction of VATTs. The method is first introduced and validated for a VATT subjected to laminar flow. Comparisons with highly-accurate body-fitted numerical models results demonstrate the method’s ability of reproducing accurately the performance and fluid mechanics of the chosen VATT. Then, the simulation of a VATT under turbulent flow is performed and comparisons with data from experiments and results from RANS-based models demonstrate the accuracy of the method. The vortex-blade interaction is visualised for various tip speed ratios and together with velocity spectra detailed insights into the fluid mechanics of VATTs are provided.

► Estimating airborne particulate emissions using a finite-volume forward solver coupled with a Bayesian inversion approach
  25 Jun, 2017
Publication date: 1 September 2017
Source:Computers & Fluids, Volume 154
Author(s): Bamdad Hosseini, John M. Stockie
We consider the problem of estimating the emissions of particulate matter from point sources at known locations. Dispersion of the particulates is modelled by the 3D advection-diffusion equation with delta-distribution source terms, as well as height-dependent advection speed and diffusion coefficients. We construct a finite volume scheme to solve this equation and apply our algorithm to an actual industrial scenario involving emissions of airborne particulates from a zinc smelter using actual wind measurements. We also address various practical considerations such as choosing appropriate methods for regularizing noisy wind data and quantifying sensitivity of the model to parameter uncertainty. Afterwards, we use the algorithm within a Bayesian framework for estimating emission rates of zinc from multiple sources over the industrial site. We compare our finite volume solver with a Gaussian plume solver within the Bayesian framework and demonstrate that the finite volume solver results in tighter uncertainty bounds on the estimated emission rates.

► New insights from high-resolution compressible DNS studies on an LPT blade boundary layer
  25 Jun, 2017
Publication date: 10 August 2017
Source:Computers & Fluids, Volume 153
Author(s): Rajesh Ranjan, S.M. Deshpande, Roddam Narasimha
Flow past the well-known low-pressure turbine blade T106A in a cascade is solved using an in-house code (named ANUROOP). This code is developed for solving 3D compressible Navier–Stokes equations and has been validated against Taylor-Green and supersonic turbulent channel flows. In order to ensure that the generally complex behaviour of the boundary layer on a turbine blade is captured with adequate precision, a hybrid grid, with a high-resolution orthogonal boundary layer mesh and hexahedral unstructured elements in the rest of the domain, is used for the simulation. Total grid size (at 161 million) is the largest used to-date for the same blade flow. Simulations are performed at Re=51,831 and angle of incidence α=45.50 without any free-stream turbulence or upstream wakes. The several new findings from the present high-resolution simulations include: (i) elimination of all significant discrepancies between the pressure distributions computed in earlier low-resolution DNS studies and experimental data, (ii) the absence of a separation bubble and transition at or near the leading edge on the suction side, (iii) the occurrence of a ‘long’ separation bubble at the trailing edge on the suction side, (iv) a demonstration of the inadequacy of classical boundary layer theory to account for the effects of blade surface curvature, and finally (v) an estimate of the curvature upto which the first correction to the boundary layer theory is adequate.

► Optimized temperature perturbation method to generate turbulent inflow conditions for LES/DNS simulations
  25 Jun, 2017
Publication date: 1 September 2017
Source:Computers & Fluids, Volume 154
Author(s): Sophia Buckingham, Lilla Koloszar, Yann Bartosiewicz, Grégoire Winckelmans
The temperature perturbation method (TPM) is used as an alternative technique to the classical velocity perturbations to generate inflow turbulence for LES or DNS simulations. The TPM consists in seeding the flow with random temperature perturbations which, through a buoyancy triggered mechanism, will induce the creation of turbulent structures. Naturally, this implies that the physical buoyancy effects need to be sufficiently strong, which has limited up to now its application to atmospheric flows. The proposed modification makes it applicable to a wider variety of wall-bounded flows, that would involve much smaller length scales than in the atmosphere. In this novel approach, a perturbation zone is defined at the entrance of the domain, along which an artificial local Richardson number is applied so that buoyancy effects are sufficiently strong to create turbulence.The TPM is implemented in the incompressible solver of OpenFOAM v2.3 with buoyancy effects and tested on a plane channel flow at Reτ=395. Prior to testing, periodic channel flow results are obtained to represent the reference fully developed turbulent state. The perturbation zone is divided into a fully active zone, where buoyancy is maximum, and a transition zone, needed to insure a smooth progression back to zero buoyancy. Several perturbation functions are applied to modulate these artificial effects, in order to identify the function that most efficiently pre-mixes the flow, thus preventing stratification effects from slowing down the flow recovery. Thereafter, the transition length and the artificial local Richardson number are optimized, based on wall shear stress recovery. Moreover, the effect of the perturbation frequency on not only the flow solution but also the energy spectra is examined in order to prevent the technique from contaminating the energy content.The flow development is compared to the synthetic turbulence generator method of Xie and Castro [1] in terms of the recovery distances of both the wall shear stress and the Reynolds stresses. The optimized method appears to be efficient with a flow that reaches equilibrium and a good quality energy spectra after about 15 δ. Although this final length remains similar to that obtained by competing methods, the optimized TPM benefits from a greater flexibility since only first-order statistics are required as input. Therefore, it can be applied without prior knowledge of second order moments or integral length scales, making it directly applicable to a wide variety of flows.

► A low-dissipative solver for turbulent compressible flows on unstructured meshes, with OpenFOAM implementation
  25 Jun, 2017
Publication date: 18 July 2017
Source:Computers & Fluids, Volume 152
Author(s): Davide Modesti, Sergio Pirozzoli
We develop a high-fidelity numerical solver for the compressible Navier–Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of the convective terms in the Navier–Stokes equations relies on a robust energy-preserving numerical flux, and numerical diffusion inherited from the AUSM scheme is added limited to the vicinity of shock waves, or wherever spurious numerical oscillations are sensed. The solver is capable of conserving the total kinetic energy in the inviscid limit, and it bears sensibly less numerical diffusion than typical industrial solvers, with incurred greater predictive power, as demonstrated through a series of test cases including DNS, LES and URANS of turbulent flows. Simplicity of implementation in existing popular solvers such as OpenFOAM is also highlighted.

► On the importance of inlet boundary conditions for aerothermal predictions of turbine stages with large eddy simulation
  25 Jun, 2017
Publication date: 1 September 2017
Source:Computers & Fluids, Volume 154
Author(s): F. Duchaine, J. Dombard, L.Y.M. Gicquel, C. Koupper
The analysis of a combustion chamber effects on the aerodynamics and thermal loads applied on a turbine stage is proposed. To do so, an integrated wall-modeled Large-Eddy Simulation of a combustion chamber simulator along with its high pressure turbine stage is performed and compared to a standalone turbine stage computation operated under the same mean conditions. For the standalone stage simulations, a parametric study of the turbulence injected at the turbine stage inlet is also discussed. For this specific configuration and with the mesh resolution used, results illustrate that the aerodynamic expansion of the turbine stage is almost insensitive to the inlet turbulent conditions. However, the temperature distribution in the turbine passages as well as on the stator and rotor walls are highly impacted by these inlet conditions underlying the importance of inlet conditions in turbine stage computations and the potential of integrated combustion chamber/turbine simulations in such a context.

► Large-eddy simulation of an air curtain confining a cavity and subjected to an external lateral flow
  25 Jun, 2017
Publication date: 18 July 2017
Source:Computers & Fluids, Volume 152
Author(s): J. Moureh, M. Yataghene
In this work, large eddy simulations of a plane jet confining a cavity and subjected to an external lateral flow (ELF) were performed. Alongside and in a complementary manner an experimental study was carried out on a scale down model (1:5) representing a generic configuration of a display case, using LDV and PIV techniques to investigate the air flow characteristics. The jet behavior is examined using the mean velocity field, the turbulence characteristics, coherent structures by using the Q-criterion, and Strouhal number. The transport of a passive scalar was also considered to illustrate the dynamic interactions between the jet and its surroundings and thus, to better investigate the effect of the ELF on the transient jet behaviour. The statistical LES results will be analyzed and validated with the experimental results and a good agreement was achieved. The results are also compared with the standard k-ε model in order to achieve a critical evaluation of this model widely used in the studied configuration. Between the two numerical methods employed, LES performs better than RANS in predicting the jet behavior and jet characteristics. In addition, LES proves its ability to predict not only self-similarity properties, but also provide the pattern of large-vortex structures and their temporal evolution, and hence, successfully resolves the transient mixing process between the jet and its surroundings with and without external perturbation.

International Journal of Computational Fluid Dynamics top

► Optimal multi-block mesh generation for CFD
  21 Jun, 2017
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► Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation
    7 Jun, 2017
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► An efficient parallel high-order compact scheme for the 3D incompressible Navier–Stokes equations
  29 May, 2017
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► High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall
  29 May, 2017
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► A coupled WC-TL SPH method for simulation of hydroelastic problems
  17 May, 2017
Volume 31, Issue 3, March 2017, Page 174-187
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► Developing a new mesh deformation technique based on support vector machine
  17 May, 2017
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► Numerical investigations of the XFEM for solving two-phase incompressible flows
  16 May, 2017
Volume 31, Issue 3, March 2017, Page 135-155
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► Effect of compressibility on plasma-based transition control for a wing with leading-edge excrescence
    3 May, 2017
Volume 31, Issue 3, March 2017, Page 156-173
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► Assessment of WENO-extended two-fluid modelling in compressible multiphase flows
  11 Apr, 2017
Volume 31, Issue 3, March 2017, Page 188-194
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► Erratum
  18 Aug, 2014
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International Journal for Numerical Methods in Fluids top

► Interface Fitted Moving Mesh Method for Axisymmetric Two-Phase Flow in Microchannels
  23 Jun, 2017

Summary

A boundary-fitted moving mesh scheme is presented for the simulation of two-phase flow in two-dimensional and axisymmetric geometries. The incompressible Navier-Stokes equations are solved using the Finite Element Method (FEM) and the mini element is used to satisfy the inf-sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data. This article is protected by copyright. All rights reserved.

► A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes
  23 Jun, 2017

Summary

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study. This article is protected by copyright. All rights reserved.

► Wall modeling via function enrichment within a high-order DG method for RANS simulations of incompressible flow
  23 Jun, 2017

Summary

We present a novel approach to wall modeling for RANS within the discontinuous Galerkin method. Wall functions are not used to prescribe boundary conditions as usual but they are built into the function space of the numerical method as a local enrichment, in addition to the standard polynomial component. The Galerkin method then automatically finds the optimal solution among all shape functions available. This idea is fully consistent and gives the wall model vast flexibility in separated boundary layers or high adverse pressure gradients. The wall model is implemented in a high-order discontinuous Galerkin solver for incompressible flow complemented by the Spalart–Allmaras closure model. As benchmark examples we present turbulent channel flow starting from Reτ=180 and up to Reτ=100,000 as well as flow past periodic hills at Reynolds numbers based on the hill height of ReH=10,595 and ReH=19,000. This article is protected by copyright. All rights reserved.

► Unified one-fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the Immersed Structural Potential Method (ISPM)
  23 Jun, 2017

Summary

In this paper, we present a two-dimensional computational framework for the simulation of fluid-structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single-phase flows. First, a variation of classical immersed techniques, pioneered with the Immersed Boundary Method [1], is presented by rearranging the governing equations which define the behaviour of the multiple physics involved. The formulation is compatible with the ‘one-fluid’ formulation for two phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the Immersed Structural Potential Method [2] developed by the authors, by adding a Level Set based method for the capturing of the fluid-fluid interfaces and an interface Lagrangian based meshless technique for the tracking of the fluid-structure interface. The spatial discretisation is based on the standard Marker-and-Cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second order time integrator and a fixed point iterative scheme. The paper presents a wide range of two-dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes. This article is protected by copyright. All rights reserved.

► An improved SPH model for multiphase flows with large density ratios
  22 Jun, 2017

Abstract

This paper presents a new SPH model for simuilating multiphase fluid flows with large density ratios. The new SPH model consists of an improved discretization scheme, an enhanced multiphase interface treatment algorithm and a coupled dynamic boundary treatment technique. The presented SPH discretization scheme is developed from Taylor series analysis with kernel normalization and kernel gradient correction, and is then used to discretize the Navier-Stokes equation to obtain improved SPH equations of motion for multiphase fluid flows. The multiphase interface treatment algorithm involves treating neighboring particles from different phases as virtual particles with specially updated density to maintain pressure consistency and a repulsive interface force between neighboring interface particles into the pressure gradient to keep sharp interface. The coupled dynamic boundary treatment technique includes a soft repulsive force between approaching fluid and solid particles while the information of virtual particles are approximated using the improved SPH discretization scheme. The presented SPH model is applied to three typical multiphase flow problems including dam breaking, Rayleigh-Taylor instability, and air bubble rising in water. It is demonstrated that inherent multiphase flow physics can be well captured while the dynamic evolution of the complex multiphase interfaces are sharp with consistent pressure across the interfaces.

► An immersed boundary solver for inviscid compressible flows
  20 Jun, 2017

Summary

In this paper, a simple and efficient immersed boundary (IB) method is developed for the numerical simulation of inviscid compressible Euler equations. We propose a method based on coordinate transformation to calculate the unknowns of ghost points. In the present study, the body-grid intercept points are used to build a complete bilinear (2-D)/trilinear (3-D) interpolation. A third-order weighted essentially nonoscillation scheme with a new reference smoothness indicator is proposed to improve the accuracy at the extrema and discontinuity region. The dynamic blocked structured adaptive mesh is used to enhance the computational efficiency. The parallel computation with loading balance is applied to save the computational cost for 3-D problems. Numerical tests show that the present method has second-order overall spatial accuracy. The double Mach reflection test indicates that the present IB method gives almost identical solution as that of the boundary-fitted method. The accuracy of the solver is further validated by subsonic and transonic flow past NACA2012 airfoil. Finally, the present IB method with adaptive mesh is validated by simulation of transonic flow past 3-D ONERA M6 Wing. Global agreement with experimental and other numerical results are obtained.

Thumbnail image of graphical abstract

An efficient ghost-cell immersed boundary method is developed for the simulation of inviscid compressible flow. We propose a method based on coordinate transformation by using the body-grid intercept points to build complete interpolation. The parallel adaptive mesh refinement is adopted to improve the computational efficiency. The figure shows the result of a 3-D simulation of transonic flow past ONERA M6 Wing.

► Improvement of the weighted essentially nonoscillatory scheme based on the interaction of smoothness indicators
  19 Jun, 2017

Abstract

The weighted essentially nonoscillatory scheme is improved by introducing new smoothness indicators that evaluate the interactions among the classical smoothness indicators suggested by Jiang and Shu. The effect of the key parameters in the new smoothness indicators on the scheme is systematically investigated. The improved scheme has smaller dissipation with larger weight assignment to the discontinuous stencils and higher numerical accuracy with weights closer to the ideal weights. To verify the theory, benchmark problems governed by the linear transport equation, the 1-dimensional nonlinear Burgers equation, and the Euler equations are conducted and analyzed, respectively. Better computational performances both on numerical resolution and accuracy are shown in the comparisons with other classical weighted essentially nonoscillatory schemes.

Thumbnail image of graphical abstract

We have proposed an improved weighted essentially nonoscillatory scheme (WENO) dubbed WENO-H by using new smoothness indicators that evaluate interactions between classical smoothness indicators suggested by Jiang and Shu. The WENO-H scheme has smaller dissipation with larger weight assignment to the discontinuous stencils and better numerical accuracy with weights closer to the ideal weights. Numerical experiments show that the improved scheme has better numerical resolution and accuracy.

► Issue Information
  16 Jun, 2017

No abstract is available for this article.

► Enhancement of the accuracy of the finite volume particle method for the simulation of incompressible flows
  16 Jun, 2017

SUMMARY

A finite volume particle (FVP) method for simulation of incompressible flows that provides enhanced accuracy is proposed. In this enhanced FVP method, a dummy neighbor particle is introduced for each particle in the calculation and used for the discretization of the gradient model and Laplacian model. The error-compensating term produced by introducing the dummy neighbor particle enables higher order terms to be calculated. The proposed gradient model and Laplacian model are applied in both pressure and pressure gradient calculations. This enhanced FVP scheme provides more accurate simulations of incompressible flows. Several 2-dimensional numerical simulations are given to confirm its enhanced performance.

Thumbnail image of graphical abstract
  1. A finite volume particle (FVP) method for simulation of incompressible flows that provides enhanced accuracy is proposed.
  2. In this enhanced FVP (EFVP) method, a dummy neighbor particle is introduced for each particle in the calculation, and higher order discretization of the gradient model and Laplacian model is realized.
  3. A numerical test to assess accuracy and convergence and several 2-dimensional numerical simulations are given to confirm its enhanced performance.
► Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization
  16 Jun, 2017

Summary

The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may use penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow-induced forces on the surface of both rigid and deforming bodies, in simulations using remeshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree-code algorithm. The viscous forces are determined by evaluating the strain-rate tensor on the surface of deforming bodies, and on a “lifted” surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow-induced surface forces. The capabilities of our method are demonstrated using simulations of self-propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.

Thumbnail image of graphical abstract

We present a method for determining flow-induced surface forces using vortex methods and Brinkman penalization. The efficacy of the method is tested for flow around rigid objects and for self-propelled swimmers. The method accurately determines force distribution on the surface of complex, temporally evolving geometries.

Journal of Computational Physics top

► Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
  25 Jun, 2017
Publication date: 15 September 2017
Source:Journal of Computational Physics, Volume 345
Author(s): Tianheng Chen, Chi-Wang Shu
It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and Shu (1994) [39]) and symmetric hyperbolic systems (Hou and Liu (2007) [36]), in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and/or when the integration is approximated by a numerical quadrature. In this paper, we develop a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in Carpenter et al. (2014) [5] and Gassner (2013) [19]. The main ingredients are summation-by-parts (SBP) operators derived from Legendre Gauss–Lobatto quadrature, the entropy conservative flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule. A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection–diffusion equations. Extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable DG methods.

► A subset multicanonical Monte Carlo method for simulating rare failure events
  25 Jun, 2017
Publication date: 1 September 2017
Source:Journal of Computational Physics, Volume 344
Author(s): Xinjuan Chen, Jinglai Li
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g. 1010). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in the entire domain of the input parameter in each iteration, the proposed subset MMC algorithm adaptively performs MMC simulations in a subset of the state space, which improves the sampling efficiency. With numerical examples we demonstrate that the proposed method is significantly more efficient than both of the SS and the MMC methods. Moreover, like the standard MMC, the proposed algorithm can reconstruct the complete distribution function of the parameter of interest and thus can provide more information than just the failure probabilities of the systems.

► The extrapolated explicit midpoint scheme for variable order and step size controlled integration of the Landau–Lifschitz–Gilbert equation
  25 Jun, 2017
Publication date: 1 October 2017
Source:Journal of Computational Physics, Volume 346
Author(s): Lukas Exl, Norbert J. Mauser, Thomas Schrefl, Dieter Suess
A practical and efficient scheme for the higher order integration of the Landau–Lifschitz–Gilbert (LLG) equation is presented. The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step and order selection. We make use of a piecewise time-linear stray field approximation to reduce the necessary work per time step. The approximation to the interpolated operator is embedded into the extrapolation process to keep in step with the hierarchic order structure of the scheme. We verify the approach by means of numerical experiments on a standardized NIST problem and compare with a higher order embedded Runge–Kutta formula. The efficiency of the presented approach increases when the stray field computation takes a larger portion of the costs for the effective field evaluation.

► High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
  25 Jun, 2017
Publication date: 15 September 2017
Source:Journal of Computational Physics, Volume 345
Author(s): Weidong Li
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners–Burggraf flow; and (c) the unsteady Taylor–Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

► Multidimensional Riemann problem with self-similar internal structure – part III – a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems
  25 Jun, 2017
Publication date: 1 October 2017
Source:Journal of Computational Physics, Volume 346
Author(s): Dinshaw S. Balsara, Boniface Nkonga
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law.The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.Several stringent test problems drawn from hydrodynamics, MHD and relativistic MHD are presented to show that the method works very well on structured meshes. Our results demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/~dbalsara/Numerical-PDE-Course.

► An efficient hybrid technique in RCS predictions of complex targets at high frequencies
  25 Jun, 2017
Publication date: 15 September 2017
Source:Journal of Computational Physics, Volume 345
Author(s): María-Jesús Algar, Lorena Lozano, Javier Morneo, Iván González, Felipe Cátedra
Most computer codes in Radar Cross Section (RCS) prediction use Physical Optics (PO) and Physical theory of Diffraction (PTD) combined with Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD). The latter approaches are computationally cheaper and much more accurate for curved surfaces, but not applicable for the computation of the RCS of all surfaces of a complex object due to the presence of caustic problems in the analysis of concave surfaces or flat surfaces in the far field. The main contribution of this paper is the development of a hybrid method based on a new combination of two asymptotic techniques: GTD and PO, considering the advantages and avoiding the disadvantages of each of them. A very efficient and accurate method to analyze the RCS of complex structures at high frequencies is obtained with the new combination. The proposed new method has been validated comparing RCS results obtained for some simple cases using the proposed approach and RCS using the rigorous technique of Method of Moments (MoM). Some complex cases have been examined at high frequencies contrasting the results with PO. This study shows the accuracy and the efficiency of the hybrid method and its suitability for the computation of the RCS at really large and complex targets at high frequencies.

► A transformed path integral approach for solution of the Fokker–Planck equation
  25 Jun, 2017
Publication date: 1 October 2017
Source:Journal of Computational Physics, Volume 346
Author(s): Gnana M. Subramaniam, Prakash Vedula
A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

► A domain integral equation approach for simulating two dimensional transverse electric scattering in a layered medium with a Gabor frame discretization
  25 Jun, 2017
Publication date: 15 September 2017
Source:Journal of Computational Physics, Volume 345
Author(s): R.J. Dilz, M.C. van Beurden
We solve the 2D transverse-electrically polarized domain-integral equation in a layered background medium by applying a Gabor frame as a projection method. This algorithm employs both a spatial and a spectral discretization of the electric field and the contrast current in the direction of the layer extent. In the spectral domain we use a representation on the complex plane that avoids the poles and branchcuts found in the Green function. Because of the special choice of the complex-plane path in the spectral domain and because of the choice to use a Gabor frame to represent functions on this path, fast algorithms based on FFTs are available to transform to and from the spectral domain, yielding an O(NlogN) scaling in computation time.

► Geometric discretization of the multidimensional Dirac delta distribution – Application to the Poisson equation with singular source terms
  25 Jun, 2017
Publication date: 1 October 2017
Source:Journal of Computational Physics, Volume 346
Author(s): Raphael Egan, Frédéric Gibou
We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

► Fast algorithms for Quadrature by Expansion I: Globally valid expansions
  25 Jun, 2017
Publication date: 15 September 2017
Source:Journal of Computational Physics, Volume 345
Author(s): Manas Rachh, Andreas Klöckner, Michael O'Neil
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method.Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.

Journal of Turbulence top

► Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence
  16 Jun, 2017
.
► Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model
  13 Jun, 2017
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► Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures
  10 Jun, 2017
.
► Numerical simulation of transitional flow on a wind turbine airfoil with RANS-based transition model
    8 Jun, 2017
.
► On the effect of an anisotropy-resolving subgrid-scale model on large eddy simulation predictions of turbulent open channel flow with wall roughness
    6 Jun, 2017
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► Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp
  31 May, 2017
Volume 18, Issue 8, August 2017, Page 781-808
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► Multi-scale interactions in a compressible boundary layer
  23 May, 2017
Volume 18, Issue 8, August 2017, Page 760-780
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► Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow
    2 May, 2017
Volume 18, Issue 8, August 2017, Page 717-759
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► Passive control of the flow around unsteady aerofoils using a self-activated deployable flap
  13 Apr, 2017
.

Physics of Fluids top

► Optimal response of Batchelor vortex
  23 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► DSMC modeling of flows with recombination reactions
  23 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Droplets passing through a soap film
  22 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Exchange flows of two immiscible Newtonian liquids in a vertical tube: From falling drops to falling slugs
  22 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Planar liquid jet: Early deformation and atomization cascades
  22 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Non-isothermal buoyancy-driven exchange flows in inclined pipes
  22 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► On the convergence of the simplified Bernoulli trial collision scheme in rarefied Fourier flow
  22 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Generation of droplets via oscillations of a tapered capillary tube filled with low-viscosity liquids
  21 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► On the linkage between the k−5/3 spectral and k−7/3 cospectral scaling in high-Reynolds number turbulent boundary layers
  21 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.
► Nonlinear processes generated by supercritical tidal flow in shallow straits
  21 Jun, 2017
Physics of Fluids, Volume 29, Issue 6, June 2017.

Theoretical and Computational Fluid Dynamics top

► Diffusional growth of cloud particles: existence and uniqueness of solutions
    8 Jun, 2017

Abstract

Diffusional growth of cloud particles is commonly described by a coupled system of parabolic equations and ordinary differential equations. The Dirichlet boundary condition for the parabolic equation is obtained from the solution of the ordinary differential equations, but this solution itself depends on the solution of the parabolic equations. We first present the governing equations describing diffusional growth of cloud particles. In a second step, we consider a simplified model problem, motivated by the diffusional growth equations. The main difference between the simplified model problem and the diffusional growth equations consists in neglecting the dependence of the domain for the parabolic equations on the solution. For the model problem, we show unique solvability using a fixed point method. Finally, we discuss application of the main result for the model problem to the diffusional growth equations and illustrate these equations with the help of a numerical solution.

► CFD study on rise and deformation characteristics of buoyancy-driven spheroid bubbles in stagnant Carreau model non-Newtonian fluids
    6 Jun, 2017

Abstract

The bubbles are almost ubiquitous in many chemical and processing industries; and many of the polymeric solutions obey non-Newtonian rheological characteristics. Therefore, in this work the rise and deformation characteristics of spheroid bubbles in Carreau model non-Newtonian fluids are numerically investigated using a level set method. To demonstrate the validity of the moving bubble interface, the present simulations are compared with existing numerical and experimental results available in the literature; and for these comparisons, the computational geometries are considered same as reported in corresponding literatures. The present bubble deformation characteristics are satisfactorily agreeing with their literature counterparts. After establishing the validity of the numerical solution procedure, the same method is applied to obtain the deformation characteristics of an air bubble in Carreau model non-Newtonian fluids. Further, the results in terms of the volume fraction images, streamlines, and viscosity profiles around the deforming bubbles are presented as function of the bubble rise time.

► Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe
    1 Jun, 2017

Abstract

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.

► Identification of flow regimes around two staggered square cylinders by a numerical study
    1 Jun, 2017

Abstract

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number ( \(Re =150\) ) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.

► On the stability of natural convection in a porous vertical slab saturated with an Oldroyd-B fluid
    1 Jun, 2017

Abstract

The stability of the conduction regime of natural convection in a porous vertical slab saturated with an Oldroyd-B fluid has been studied. A modified Darcy’s law is utilized to describe the flow in a porous medium. The eigenvalue problem is solved using Chebyshev collocation method and the critical Darcy–Rayleigh number with respect to the wave number is extracted for different values of physical parameters. Despite the basic state being the same for Newtonian and Oldroyd-B fluids, it is observed that the basic flow is unstable for viscoelastic fluids—a result of contrast compared to Newtonian as well as for power-law fluids. It is found that the viscoelasticity parameters exhibit both stabilizing and destabilizing influence on the system. Increase in the value of strain retardation parameter \(\Lambda _2 \) portrays stabilizing influence on the system while increasing stress relaxation parameter \(\Lambda _1\) displays an opposite trend. Also, the effect of increasing ratio of heat capacities is to delay the onset of instability. The results for Maxwell fluid obtained as a particular case from the present study indicate that the system is more unstable compared to Oldroyd-B fluid.

► Numerical modeling of the impact pressure in a compressible liquid medium: application to the slap phase of the locomotion of a basilisk lizard
    1 Jun, 2017

Abstract

The forces acting on a solid body just at the time of impact on the surface of a medium with very low compressibility, such as water, can be quantified at acoustic time scales. This is necessary in wide range of applications varying from large-scale ship designs to the walking or running mechanisms of small creatures such as the basilisk lizard. In order to characterize such forces, a numerical model is developed in this study and is validated using analytical expressions of pressure as a function of the speed of sound-wave propagation in water. The computational results not only accurately match the analytical values but are also able to effectively capture the propagation of acoustic waves in water. The model is further applied to a case study wherein the impact impulse required by the basilisk lizard to assist in its walking on the water surface is evaluated. The numerical results are found to be in agreement with the closest available experimental data. The model and approach are thus proposed to evaluate impact forces for wide range of applications.

► Influence of hydrodynamic slip on convective transport in flow past a circular cylinder
    1 Jun, 2017

Abstract

The presence of a finite tangential velocity on a hydrodynamically slipping surface is known to reduce vorticity production in bluff body flows substantially while at the same time enhancing its convection downstream and into the wake. Here, we investigate the effect of hydrodynamic slippage on the convective heat transfer (scalar transport) from a heated isothermal circular cylinder placed in a uniform cross-flow of an incompressible fluid through analytical and simulation techniques. At low Reynolds ( \({\textit{Re}}\ll 1\) ) and high Péclet ( \({\textit{Pe}}\gg 1\) ) numbers, our theoretical analysis based on Oseen and thermal boundary layer equations allows for an explicit determination of the dependence of the thermal transport on the non-dimensional slip length \(l_s\) . In this case, the surface-averaged Nusselt number, Nu transitions gradually between the asymptotic limits of \(Nu \sim {\textit{Pe}}^{1/3}\) and \(Nu \sim {\textit{Pe}}^{1/2}\) for no-slip ( \(l_s \rightarrow 0\) ) and shear-free ( \(l_s \rightarrow \infty \) ) boundaries, respectively. Boundary layer analysis also shows that the scaling \(Nu \sim {\textit{Pe}}^{1/2}\) holds for a shear-free cylinder surface in the asymptotic limit of \({\textit{Re}}\gg 1\) so that the corresponding heat transfer rate becomes independent of the fluid viscosity. At finite \({\textit{Re}}\) , results from our two-dimensional simulations confirm the scaling \(Nu \sim {\textit{Pe}}^{1/2}\) for a shear-free boundary over the range \(0.1 \le {\textit{Re}}\le 10^3\) and \(0.1\le {\textit{Pr}}\le 10\) . A gradual transition from the lower asymptotic limit corresponding to a no-slip surface, to the upper limit for a shear-free boundary, with \(l_s\) , is observed in both the maximum slip velocity and the Nu. The local time-averaged Nusselt number \(Nu_{\theta }\) for a shear-free surface exceeds the one for a no-slip surface all along the cylinder boundary except over the downstream portion where unsteady separation and flow reversal lead to an appreciable rise in the local heat transfer rates, especially at high \({\textit{Re}}\) and Pr. At a Reynolds number of \(10^3\) , the formation of secondary recirculating eddy pairs results in appearance of additional local maxima in \(Nu_{\theta }\) at locations that are in close proximity to the mean secondary stagnation points. As a consequence, Nu exhibits a non-monotonic variation with \(l_s\) increasing initially from its lowermost value for a no-slip surface and then decreasing before rising gradually toward the upper asymptotic limit for a shear-free cylinder. A non-monotonic dependence of the spanwise-averaged Nu on \(l_s\) is observed in three dimensions as well with the three-dimensional wake instabilities that appear at sufficiently low \(l_s\) , strongly influencing the convective thermal transport from the cylinder. The analogy between heat transfer and single-component mass transfer implies that our results can directly be applied to determine the dependency of convective mass transfer of a single solute on hydrodynamic slip length in similar configurations through straightforward replacement of Nu and \({\textit{Pr}}\) with Sherwood and Schmidt numbers, respectively.

► Use of natural instabilities for generation of streamwise vortices in a laminar channel flow
    1 Jun, 2017

Abstract

An analysis of pressure-gradient-driven flows in channels with walls modified by transverse ribs has been carried out. The ribs have been introduced intentionally in order to generate streamwise vortices through centrifugally driven instabilities. The cost of their introduction, i.e. the additional pressure losses, have been determined. Linear stability theory has been used to determine conditions required for the formation of the vortices. It has been demonstrated that there exists a finite range of rib wave numbers capable of creating vortices. Within this range, there exists an optimal wave number which results in the minimum critical Reynolds number for the specified rib amplitude. The optimal wave numbers marginally depend on the rib positions and amplitudes. As the formation of the vortices can be interfered with by viscosity-driven instabilities, the critical conditions for the onset of such instabilities have also been determined. The rib geometries which result in the vortex formation with the smallest drag penalty and without interference from the viscosity-driven instabilities have been identified.

► The linearized pressure Poisson equation for global instability analysis of incompressible flows
  16 May, 2017

Abstract

The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

► A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization
  29 Apr, 2017

Abstract

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\) . Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.


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