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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

► Settling behavior of two particles with different densities in a vertical channel
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): Deming Nie, Jianzhong Lin, Qi Gao
Sedimentation of two particles with different densities in a two-dimensional channel is studied using the lattice Boltzmann method. We focus on the steady state and periodic state of the settling behavior of the particles, which strongly depend on the Reynolds number Re as well as the density difference α. We show that the particles always reach a steady state if α is small enough at a large Re, while they are predicted to oscillate at a small Re. The staggered configurations in steady state for a wide range of Re and α are presented. Our results also demonstrate that the periodic state of the particles at a small Re is different from that at large Re. One significant difference is that the amplitude of oscillation decreases as α increases when Re is small, while the opposite is true when Re is large. In addition, there exists a narrow range of Re within which we can observe both of the above-mentioned periodic states. At large Re, the effect of α on the periodic motion of particles is quite significant. The phase diagram, constructed using the lateral displacements of the two particles, shows a transition to a period-doubled state on increasing α when Re is large.

► On the development of an efficient numerical ice tank for the simulation of fluid-ship-rigid-ice interactions on graphics processing units
  19 Aug, 2017
Publication date: 20 September 2017
Source:Computers & Fluids, Volume 155
Author(s): Christian F. Janßen, Dennis Mierke, Thomas Rung
This paper reports on the adaptation of a Lattice Boltzmann based free surface flow solver to the simulation of complex fluid-ship-ice interactions in marine engineering. The analysis is restricted to the interaction of already broken ice floes and the ship hull, aiming at the optimization of a ship hull’s capability to clear the ice and keep it away from the propulsion device. The ice floes and the ship hull are treated as rigid bodies. In order to model the dynamics of the colliding rigid multi-body systems, a coupling of the flow solver to the Open Dynamics Engine (ODE) is established. The basic methodology and initial validation of the fluid-structure coupling is presented. Then, basic validations of the employed collision and friction models are given, particularly focusing on interacting surface triangle meshes that later serve to describe the ice floes. Finally, a three-dimensional validation case shows that the ship-fluid-rigid-ice interaction forces agree well with available reference data. Apart from the numerical coupling, performance has to be addressed. The employed flow solver elbe uses graphics processing units (GPUs) to accelerate the numerical calculations. In order to make the GPU performance accessible to colliding multi-body systems, a careful and tailor-made implementation is presented in the paper. The resulting optimized elbe-ODE solver allows for the investigation of three-dimensional fluid-ship-ice interactions in a very competitive computational time, on off-the-shelf desktop hardware.

► An efficient flamelet progress-variable method for modeling non-premixed flames in weak electric fields
  19 Aug, 2017
Publication date: 3 November 2017
Source:Computers & Fluids, Volume 157
Author(s): M. Di Renzo, P. De Palma, M.D. de Tullio, G. Pascazio
Combustion stabilization and enhancement of the flammability limits are mandatory objectives to improve nowadays combustion chambers. At this purpose, the use of an electric field in the flame region provides a solution which is, at the same time, easy to implement and effective to modify the flame structure. The present work describes an efficient flamelet progress-variable approach developed to model the fluid dynamics of flames immersed in an electric field. The main feature of this model is that it can use complex ionization mechanisms without increasing the computational cost of the simulation. The model is based on the assumption that the combustion process is not directly influenced by the electric field and has been tested using two chemi-ionization mechanisms of different complexity in order to examine its behavior with and without the presence of heavy anions in the mixture. Using a one- and a two-dimensional numerical test cases, the present approach has been able to reproduce all the major aspects encountered when a flame is subject to an imposed electric field and the main effects of the different chemical mechanisms. Moreover, the proposed model is shown to produce a large reduction in the computational cost, being able to shorten the time needed to perform a simulation up to 40 times.

► Stochastic representation of the Reynolds transport theorem: Revisiting large-scale modeling
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): S. Kadri Harouna, E. Mémin
We explore the potential of a formulation of the Navier-Stokes equations incorporating a random description of the small-scale velocity component. This model, established from a version of the Reynolds transport theorem adapted to a stochastic representation of the flow, gives rise to a large-scale description of the flow dynamics in which emerges an anisotropic subgrid tensor, reminiscent to the Reynolds stress tensor, together with a drift correction due to an inhomogeneous turbulence. The corresponding subgrid model, which depends on the small scales velocity variance, generalizes the Boussinesq eddy viscosity assumption. However, it is not anymore obtained from an analogy with molecular dissipation but ensues rigorously from the random modeling of the flow. This principle allows us to propose several subgrid models defined directly on the resolved flow component. We assess and compare numerically those models on a standard Green-Taylor vortex flow at Reynolds numbers Re  = 1600, Re= 3000 and Re = 5000. The numerical simulations, carried out with an accurate divergence-free scheme, outperform classical large-eddies formulations and provides a simple demonstration of the pertinence of the proposed large-scale modeling.

► Development of an efficient bifurcation tracking method
  19 Aug, 2017
Publication date: 3 November 2017
Source:Computers & Fluids, Volume 157
Author(s): S.J. Huntley, D.P. Jones, A.L. Gaitonde
The buffet onset boundary is associated with a change in stability of the flow solution. The buffet onset boundary has been computed for a NACA 0012 aerofoil using a modified bifurcation tracking method. The algorithm combines the projection aspect of the Recursive Projection Method with two different direct bifurcation tracking methods. This considerably reduces the cost of the bifurcation tracking methods by solving for the bifurcation point on a small subspace of the system containing only the least stable dynamics. The method has been extended to allow the boundary to be computed as geometrical parameters, camber and thickness, are changed. This enables rapid evaluation of the effect of different aerofoil designs on the boundary. Results are presented comparing the full bifurcation tracking methods to their projected equivalent and show that although the projected methods lack the numerical accuracy of the full counterpart, the trends of the boundaries agree well.

► Enhancement of propulsive performance of flapping foil by fish-like motion pattern
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): H.R. Karbasian, J.A. Esfahani
In this study, the flapping foil propulsion with a novel motion pattern is numerically investigated. The proposed motion pattern is inspired from kinematics of fish species, such as marine mammals, utilizing a foil-shaped tail to swim in aquatic environments. This motion pattern is named as fish-like flapping foil and causes the swimming kinematics to be more complex. The numerical simulation for a two dimensional NACA 0012 is conducted using computational fluid dynamics (CFD) approaches at relatively low Reynolds number of 4 × 104. The results show that proposed motion pattern would change the angle of attack profile notably. It is found that the motion trajectory as well as angle of attack profile affect the flow structure around the foil and increase the hydrodynamic loads. In this kinematic model the vortex strength and pattern of vortex evolution might change. It is observed that the proposed model for flapping foil could significantly enhance the propulsive efficiency in certain conditions (as considered in this paper), which makes it possible to apply this kind of model in order to improve propulsion performance of devices in aquatic environments.

► A comparative study of boundary conditions for lattice Boltzmann simulations of high Reynolds number flows
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): Kainan Hu, Jianping Meng, Hongwu Zhang, Xiao-Jun Gu, David R Emerson, Yonghao Zhang
Four commonly-used boundary conditions in lattice Boltzmann simulation, i.e. the bounce-back, non-equilibrium bounce-back, non-equilibrium extrapolation, and the kinetic boundary condition, have been systematically investigated to assess their accuracy, stability and efficiency in simulating high Reynolds number flows. For the classical lid-driven cavity flow problem, it is found that the bounce-back scheme does not influence the simulation accuracy in the bulk region if the boundary condition is properly implemented to avoid generating non-physical slip velocity. Although the kinetic boundary condition naturally produces physical slip velocity at the wall, it gives overall satisfactory predictions of the center-line velocity profile and the vortex center locations for the Reynolds numbers considered. For the cavity flow problem, all four boundary conditions show minimal difference in the computing time needed to reach a steady state. This is surprising because the kinetic boundary condition is significantly different from the other three schemes which are designed specifically for no-slip boundary conditions. The bounce-back scheme is the most computationally efficient in updating boundary points, which is particularly attractive if there are a large number of solid bodies in the flow field. For the numerical stability, we further test the pressure-driven channel flow with or without a enclosed square cylinder. Overall, the kinetic boundary condition is the most stable of the four schemes. The non-equilibrium extrapolation scheme presents excellent stability second to the kinetic boundary condition for the lid-driven cavity flow. In comparison with other threes schemes, the stability of non-equilibrium bounce-back scheme appears to be less satisfactory for both flows.

► Hermite Upwind Positive Schemes (HUPS) for non-linear hyperbolic systems of conservation laws
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): G. Capdeville
This work aims at designing a numerical model for discretizing, over compact stencils, non-linear hyperbolic systems of conservation laws, with high-order accuracy, while maintaining a positivity property of the discretization.Starting from a multi-dimensional finite volume discretization of the PDEs, we build an Hermitian polynomial based upon a least-square procedure. This polynomial is then used to interpolate, with a fourth-order accuracy, the pointwise quantities (variable and its first derivatives) that are necessary to compute the numerical fluxes at cell interfaces.A monotonicity-preserving algorithm helps to enforce the positivity of the resulting spatial discretization.Each variable of the problem and its first derivatives are then evolved in time by using a fourth-order positive Runge–Kutta algorithm (SSPRK).The resulting scheme is a fourth-order least-square Hermitian Upwind Positive Scheme (HUPS).Extensive numerical 2D tests for scalar or Euler equations of gas dynamics are driven in order to assess the potentialities of the method.

► Optimization of spray break-up CFD simulations by combining Σ-Y Eulerian atomization model with a response surface methodology under diesel engine-like conditions (ECN Spray A)
  19 Aug, 2017
Publication date: 12 October 2017
Source:Computers & Fluids, Volume 156
Author(s): A. Pandal, R. Payri, J.M. García-Oliver, J.M. Pastor
This work evaluates the performance of the Σ-Y Eulerian atomization model at reproducing the internal structure of a diesel spray with a special focus on Sauter Mean Diameter (SMD) predictions. Modeling results have been compared to x-ray radiography measurements [21,24,38] which provided unique data within dense spray region. The first step corresponds to accurately reproduce the large scale spray dispersion. Among different RANS turbulence models, the standard k-ε with the round jet corrected C value (1.60), has shown the best performance, as shown in [12]. Then, the study is devoted to the application and optimization of the predicted interphase surface density (Σ). In this work, a combination of CFD modeling and the statistical Design of Experiments (DOE) technique known as Response Surface Method (RSM) is applied in order to improve Sauter Mean Diameter (SMD) predictions from Σ equation compared to experimental measurements. In the investigation, two different optimizations are conducted for the three modeling parameters involved in the equation, following a Central Composite Design (CCD), leading to 15 simulations for each one. After that, both optimum sets of values are validated to assure the accuracy of the method and it is decided the best choice. Finally, different injection and ambient conditions are simulated, with those selected values, providing a remarkable improvement in the modeling performance.

► Editorial Board
  19 Aug, 2017
Publication date: 20 September 2017
Source:Computers & Fluids, Volume 155



International Journal of Computational Fluid Dynamics top

► On the influences of key modelling constants of large eddy simulations for large-scale compartment fires predictions
    2 Aug, 2017
Volume 31, Issue 6-8, July - September 2017, Page 324-337
.
► Efficient simulation of multidimensional continuum and non-continuum flows by a parallelised unified gas kinetic scheme solver
  14 Jul, 2017
Volume 31, Issue 6-8, July - September 2017, Page 292-309
.
► A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows
  13 Jul, 2017
Volume 31, Issue 6-8, July - September 2017, Page 269-291
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► Curvature effect on droplet impacting onto hydrophobic and superhydrophobic spheres
    7 Jul, 2017
Volume 31, Issue 6-8, July - September 2017, Page 310-323
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► Erratum
  18 Aug, 2014
.

International Journal for Numerical Methods in Fluids top

► Fluid-structure coupling of linear elastic model with compressible flow models
  18 Aug, 2017

Summary

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose we employ a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of two fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi-1D problems for which an explicit solution can be determined. For a more realistic scenario a 2D application is considered where in a compressible single fluid a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure. This article is protected by copyright. All rights reserved.

► Feedback control of laminar flow separation on NACA23012 airfoil by POD analysis and using perturbed Navier-Stokes equations
  17 Aug, 2017

Summary

The main purpose of this article is to develop a forced reduced-order model based on the proper orthogonal decomposition (POD)/Galerkin projection (on isentropic Navier-Stokes equations) and perturbation method on the compressible Navier-Stokes equations. The resulting forced reduced-order model will be used in optimal control of the separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 800, and high incidence angle of 24°. The main disadvantage of the POD/Galerkin projection method for control purposes is that controlling parameters do not show up explicitly in the resulting reduced-order system. The perturbation method and POD/Galerkin projection on the isentropic Navier-Stokes equations introduce a forced reduced-order model that can predict the time varying influence of the controlling parameters and the Navier-Stokes response to external excitations. An optimal control theory based on forced reduced-order system is used to design a control law for a nonlinear reduced-order system, which attempts to minimize the vorticity content in the flow field. The test bed is a laminar flow over NACA23012 airfoil actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. The results show that wall jet can significantly influence the flow field, remove separation bubbles, and increase the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate manner.

Thumbnail image of graphical abstract

The main purpose of this article is to develop a forced reduced-order model based on the proper orthogonal decomposition/Galerkin projection and perturbation method on the compressible Navier-Stokes equations. The model will be used in optimal control of the laminar separated flow over a NACA23012 airfoil at M = 0.2, Re = 800, and incidence angle of 24°. The airfoil is actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge.

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

Summary

We present a novel approach to wall modeling for the Reynolds-averaged Navier-Stokes equations 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=100000 as well as flow past periodic hills at Reynolds numbers based on the hill height of ReH=10595 and ReH=19000.

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We present a novel approach to wall modeling for the Reynolds-averaged Navier-Stokes equations within the discontinuous Galerkin method. The velocity profile in a turbulent boundary layer is composed of the standard polynomial component plus an enrichment component, which is constructed using Spalding's law-of-the-wall. This composition results in a much higher degree of flexibility in strong nonequilibrium boundary layers and mesh independence than common wall functions can provide.

► Issue Information
  15 Aug, 2017

No abstract is available for this article.

► Simplex space-time meshes in two-phase flow simulations
  15 Aug, 2017

Summary

In this paper, we present the numerical solution of 2-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Arbitrary temporal refinement is applied to preselected regions of the mesh and is governed by a quantity that is part of the solution process, namely, the interface position in 2-phase flow. Because of local effects such as surface tension, jumps in material properties, etc, the interface can in general be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying 2-phase flow problems.

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The main goal of this paper was to demonstrate how adaptive temporal refinement can be applied in the area of evolving fronts, by means of space-time FE. Firstly, tetrahedral (2D) and pentatope (3D) meshes are used for simulating two-phase flow problems and their behavior is compared to that of the usual prismatic space-time elements. Furthermore, a hybrid tetrahedral space-time grid is used for the filling of a step cavity, giving us the flexibility to use a type of local time-stepping.

► Model identification of reduced order fluid dynamics systems using deep learning
  14 Aug, 2017

Summary

This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The deep learning approach is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the nonlinear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The long short-term memory network is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system.

The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.

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This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.

► A high-order flux reconstruction adaptive mesh refinement method for magnetohydrodynamics on unstructured grids
    7 Aug, 2017

Summary

We report our recent development of the high-order flux reconstruction adaptive mesh refinement (AMR) method for magnetohydrodynamics (MHD). The resulted framework features a shock-capturing duo of AMR and artificial resistivity (AR), which can robustly capture shocks and rotational and contact discontinuities with a fraction of the cell counts that are usually required. In our previous paper, we have presented a shock-capturing framework on hydrodynamic problems with artificial diffusivity and AMR. Our AMR approach features a tree-free, direct-addressing approach in retrieving data across multiple levels of refinement. In this article, we report an extension to MHD systems that retains the flexibility of using unstructured grids. The challenges due to complex shock structures and divergence-free constraint of magnetic field are more difficult to deal with than those of hydrodynamic systems. The accuracy of our solver hinges on 2 properties to achieve high-order accuracy on MHD systems: removing the divergence error thoroughly and resolving discontinuities accurately. A hyperbolic divergence cleaning method with multiple subiterations is used for the first task. This method drives away the divergence error and preserves conservative forms of the governing equations. The subiteration can be accelerated by absorbing a pseudo time step into the wave speed coefficient, therefore enjoys a relaxed CFL condition. The AMR method rallies multiple levels of refined cells around various shock discontinuities, and it coordinates with the AR method to obtain sharp shock profiles. The physically consistent AR method localizes discontinuities and damps the spurious oscillation arising in the curl of the magnetic field. The effectiveness of the AMR and AR combination is demonstrated to be much more powerful than simply adding AR on finer and finer mesh, since the AMR steeply reduces the required amount of AR and confines the added artificial diffusivity and resistivity to a narrower and narrower region. We are able to verify the designed high-order accuracy in space by using smooth flow test problems on unstructured grids. The efficiency and robustness of this framework are fully demonstrated through a number of two-dimensional nonsmooth ideal MHD tests. We also successfully demonstrate that the AMR method can help significantly save computational cost for the Orszag-Tang vortex problem.

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High-order flux reconstruction method is extended for solving magnetohydrodynamic equations for the first time. The shock-capturing duo of adaptive mesh refinement and artificial resistivity achieves sharply defined shock profile with a fraction of cells of uniformly refined cell, as shown in the above Orszag-Tang vortex case. When plasma beta is low, a decoupled hyperbolic cleaning method is capable of thoroughly removing the divergence error in a multiple sweep fashion.

► Unified one-fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)
    7 Aug, 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 (IBM), 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 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 d range of two-dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.

Thumbnail image of graphical abstract

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. The numerical technique followed in this paper builds upon the Immersed Structural Potential Method 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.

► Portable data-parallel surface reconstruction on a uniform rectilinear grid
    7 Aug, 2017

Summary

With the increasing heterogeneity and on-node parallelism of high-performance computing hardware, a major challenge is to develop portable and efficient algorithms and software. In this work, we present our implementation of a portable code to perform surface reconstruction using NVIDIA's Thrust library. Surface reconstruction is a technique commonly used in volume tracking methods for simulations of multimaterial flow with interfaces. We have designed a 3D mesh data structure that is easily mapped to the 1D vectors used by Thrust and at the same time is simple to use and uses familiar data structure terminology (such as cells, faces, vertices, and edges). With this new data structure in place, we have implemented a piecewise linear interface reconstruction algorithm in 3 dimensions that effectively exploits the symmetry present in a uniform rectilinear computational cell. Finally, we report performance results, which show that a single implementation of these algorithms can be compiled to multiple backends (specifically, multi-core CPUs, NVIDIA GPUs, and Intel Xeon Phi processors), making efficient use of the available parallelism on each. We also compare performance of our implementation to a legacy FORTRAN implementation in Message Passing Interface (MPI) and show performance parity on single and multi-core CPU and achieved good parallel speed-ups on GPU. Our research demonstrates the advantage of performance portability of the underlying data-parallel programming model.

Thumbnail image of graphical abstract

In this work, we present the implementation of a portable code PINION to perform surface reconstruction using NVIDIA's Thrust Library. Performance comparison of the RAGE and PINION codes for a sphere of radius 0.25 (A) and 0.45 (B), a cylinder (C), and the Stanford bunny (D) is given in the above Figure.

► A Generalized Rusanov Method for the Baer-Nunziato Equations with Application to DDT Processes in Condensed Porous Explosives
    2 Aug, 2017

Summary

The paper addresses a numerical approach for solving the Baer-Nunziato equations describing compressible two-phase flows. We are developing a finite-volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer-Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration-to-detonation transition (DDT) in porous reactive materials.

Journal of Computational Physics top

► A parallel orbital-updating based plane-wave basis method for electronic structure calculations
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): Yan Pan, Xiaoying Dai, Stefano de Gironcoli, Xin-Gao Gong, Gian-Marco Rignanese, Aihui Zhou
Motivated by the recently proposed parallel orbital-updating approach in real space method [1], we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

► Unconditionally stable Gauge–Uzawa finite element schemes for incompressible natural convection problems with variable density
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): Jilian Wu, Jie Shen, Xinlong Feng
We construct in this paper two Gauge–Uzawa schemes, one in conserved form and the other in convective form, for solving natural convection problems with variable density, and prove that the first-order versions of both schemes are unconditionally stable. We also show that a full discretized version of the conserved scheme with finite elements is also unconditionally stable. These schemes lead to a sequence of decoupled elliptic equations to solve at each step, hence, they are very efficient and easy to implement. We present several numerical tests to validate the analysis and demonstrate the effectiveness of these schemes for simulating natural convection problems with large density differences.

► Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm
  22 Aug, 2017
Publication date: 15 November 2017
Source:Journal of Computational Physics, Volume 349
Author(s): David J. Munk, Timoleon Kipouros, Gareth A. Vio, Grant P. Steven, Geoffrey T. Parks
Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses in the casing are as uniform as possible, thus giving a desired operating life with minimum weight.The ultimate aim of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multidisciplinary optimisation problems. This is achieved by developing a bi-directional evolutionary structural optimisation algorithm that is directly coupled to the Lattice Boltzmann method, used for simulating the flow in the micro fluidic device, for the objectives of minimum compliance and maximum vorticity. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms, such as genetic algorithms, particle swarms and Tabu Searches, less efficient for this task.The multidisciplinary topology optimisation framework presented in this article is shown to increase the stiffness of the structure from the datum case and produce physically acceptable designs. Furthermore, the topology optimisation method outperforms a Tabu Search algorithm in designing the baffle to maximise the mixing of the two fluids.

► A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): Benjamin Krank, Niklas Fehn, Wolfgang A. Wall, Martin Kronbichler
We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier–Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad–div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ=180 as well as 590.

► A locally p-adaptive approach for Large Eddy Simulation of compressible flows in a DG framework
  22 Aug, 2017
Publication date: 15 November 2017
Source:Journal of Computational Physics, Volume 349
Author(s): Matteo Tugnoli, Antonella Abbà, Luca Bonaventura, Marco Restelli
We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high-order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already employed in the literature. The resulting locally adaptive approach allows to achieve significant reductions in computational cost of representative LES computations.

► Efficient mesh motion using radial basis functions with volume grid points reduction algorithm
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): Liang Xie, Hong Liu
As one of the most robust mesh deformation technique available, the radial basis function (RBF) mesh deformation has been accepted widely. However, for volume mesh deformation driven by surface motion, the RBF system may become impractical for large meshes due to the large number of both surface (control) points and volume points. Surface points selection procedure based on the greedy algorithm results in an efficient implementation of the RBF-based mesh deformation procedure. The greedy algorithm could reduce the number of surface points involved in the RBF interpolation while acquire an acceptable accuracy as shown in literature. To improve the efficiency of the RBF method furthermore, an issue that how to reduce the number of the volume points needed to be moved is addressed. In this paper, we propose an algorithm for volume points reduction based on a wall distance based restricting function which is added to the formulation of the RBF based interpolation. This restricting function is firstly introduced by the current article. To support large deformation, a multi-level subspace interpolation is essentially needed, although this technique was used to improve the efficiency of the surface points selection procedure in the existed literature. The key point of this technique is setting the error of previous interpolation step as the object of current step, and restricting interpolation region gradually. Because the tolerance of the error is decreased hierarchically, the number of the surface points is increased but the number of the volume points needed to be moved is reduced gradually. Therefore, the CPU cost of updating the mesh motion could be reduced eventually since it scales with the product of these two numbers. The computational requirement of the proposed procedure is reduced evidently compared with the standard procedure as proved by some examples.

► Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification
  22 Aug, 2017
Publication date: 15 November 2017
Source:Journal of Computational Physics, Volume 349
Author(s): M. Arnst, B. Abello Álvarez, J.-P. Ponthot, R. Boman
This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis–Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

► The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): V. Gyrya, K. Lipnikov
We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

► Numerical study on the convergence to steady state solutions of a new class of high order WENO schemes
  22 Aug, 2017
Publication date: 15 November 2017
Source:Journal of Computational Physics, Volume 349
Author(s): Jun Zhu, Chi-Wang Shu
A new class of high order weighted essentially non-oscillatory (WENO) schemes (Zhu and Qiu, 2016, [50]) is applied to solve Euler equations with steady state solutions. It is known that the classical WENO schemes (Jiang and Shu, 1996, [23]) might suffer from slight post-shock oscillations. Even though such post-shock oscillations are small enough in magnitude and do not visually affect the essentially non-oscillatory property, they are truly responsible for the residue to hang at a truncation error level instead of converging to machine zero. With the application of this new class of WENO schemes, such slight post-shock oscillations are essentially removed and the residue can settle down to machine zero in steady state simulations. This new class of WENO schemes uses a convex combination of a quartic polynomial with two linear polynomials on unequal size spatial stencils in one dimension and is extended to two dimensions in a dimension-by-dimension fashion. By doing so, such WENO schemes use the same information as the classical WENO schemes in Jiang and Shu (1996) [23] and yield the same formal order of accuracy in smooth regions, yet they could converge to steady state solutions with very tiny residue close to machine zero for our extensive list of test problems including shocks, contact discontinuities, rarefaction waves or their interactions, and with these complex waves passing through the boundaries of the computational domain.

► Coupled variational formulations of linear elasticity and the DPG methodology
  22 Aug, 2017
Publication date: 1 November 2017
Source:Journal of Computational Physics, Volume 348
Author(s): Federico Fuentes, Brendan Keith, Leszek Demkowicz, Patrick Le Tallec
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually well-posed family of broken variational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where stability or a particular mode of convergence is desired in a part of the domain. The linear elasticity equations are solved in this work, but the approach can be applied to other equations as well. The broken variational formulations, which are essentially extensions of more standard formulations, are characterized by the presence of mesh-dependent broken test spaces and interface trial variables at the boundaries of the elements of the mesh. This allows necessary information to be naturally transmitted between adjacent subdomains, resulting in coupled variational formulations which are then proved to be globally well-posed. They are solved numerically using the DPG methodology, which is especially crafted to produce stable discretizations of broken formulations. Finally, expected convergence rates are verified in two different and illustrative examples.

Journal of Turbulence top

► Phase-relationships between scales in the perturbed turbulent boundary layer
  14 Aug, 2017
.
► Eulerian spatial and temporal autocorrelations: assessment of Taylor's hypothesis and a model
    9 Aug, 2017
.
► Hot-wire and PIV characterisation of a novel small-scale turbulent channel flow facility developed to study premixed expanding flames
    2 Aug, 2017
.
► Analysis of turbulent axisymmetric inner near wake
  31 Jul, 2017
.
► Turbulent scalar flux transport in head-on quenching of turbulent premixed flames: a direct numerical simulations approach to assess models for Reynolds averaged Navier Stokes simulations
  21 Jul, 2017
.
► Analysis of structure function equations up to the seventh order
    6 Jul, 2017
.
► Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation
  29 Jun, 2017
.
► Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology
  29 Jun, 2017
.
► Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence
  16 Jun, 2017
Volume 18, Issue 9, September 2017, Page 825-853
.
► Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model
  13 Jun, 2017
.

Physics of Fluids top

► Cylindrical shock waves in rotational axisymmetric non-ideal dusty gas with increasing energy under the action of monochromatic radiation
  22 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Quantitative analysis of non-equilibrium phase transition process by the catastrophe theory
  21 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Measurement of turbulent spatial structure and kinetic energy spectrum by exact temporal-to-spatial mapping
  21 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Scalar transport and the validity of Damköhler’s hypotheses for flame propagation in intense turbulence
  21 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Homogeneous cooling state of dilute granular gases of charged particles
  21 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Unsteady flow of a thixotropic fluid in a slowly varying pipe
  21 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Why do we live for much less than 100 years? A fluid mechanics view and approach
  18 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► Characterization of interfacial waves and pressure drop in horizontal oil-water core-annular flows
  18 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► A smoothed particle hydrodynamics (SPH) study of sediment dispersion on the seafloor
  18 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.
► The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets
  18 Aug, 2017
Physics of Fluids, Volume 29, Issue 8, August 2017.

Theoretical and Computational Fluid Dynamics top

► Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows
  14 Aug, 2017

Abstract

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.

► Particle–boundary interaction in a shear-driven cavity flow
    1 Aug, 2017

Abstract

The motion of a heavy finite-size tracer is numerically calculated in a two-dimensional shear-driven cavity. The particle motion is computed using a discontinuous Galerkin-finite-element method combined with a smoothed profile method resolving all scales, including the flow in the lubrication gap between the particle and the boundary. The centrifugation of heavy particles in the recirculating flow is counteracted by a repulsion from the shear-stress surface. The resulting limit cycle for the particle motion represents an attractor for particles in dilute suspensions. The limit cycles obtained by fully resolved simulations as a function of the particle size and density are compared with those obtained by one-way coupling using the Maxey–Riley equation and an inelastic collision model for the particle–boundary interaction, solely characterized by an interaction-length parameter. It is shown that the one-way coupling approach can faithfully approximate the true limit cycle if the interaction length is selected depending on the particle size and its relative density.

► Saddle point of attachment in jet–crossflow interaction
    1 Aug, 2017

Abstract

Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.

► On the odd and even secondary instabilities of Görtler vortices
    1 Aug, 2017

Abstract

Boundary layer flows over concave wall can be unstable to disturbances giving rise to streamwise counter-rotating vortices known as Görtler vortices. These vortices in its nonlinear form are responsible for a strong distortion of the streamwise velocity profiles in the wall-normal and spanwise directions. The resulting inflectional velocity profiles are unstable to unsteady disturbances. These disturbances are called secondary instabilities and can develop into horseshoe vortices or a sinuous motion of the Görtler vortices. These types of secondary instabilities are known as even (varicose) and odd (sinuous) modes, respectively. Although many studies focused this subject, it has not been stated which mode dominates the transition process. In the present study the secondary instability of Görtler flow is investigated using high-order spatial numerical simulation. Multi-frequency unsteady disturbances are introduced with the same spanwise wavelength as the Görtler vortices, but different spanwise phases. Three different spanwise phases are used and the effect on the secondary instability is analyzed. Both, even and odd secondary instabilities are observed, according to the relative spanwise position of the unsteady disturbances. The growth analysis for each secondary crossplane instability mode is made using a temporal Fourier analysis and the physics is explored with the aid of the flow structures visualization. The results introducing disturbances that give rise to odd and even modes simultaneously show that, for the spanwise wavelength analyzed, the odd modes grow first and dominate the transition process.

► Time-dependent modeling of oscillatory instability of three-dimensional natural convection of air in a laterally heated cubic box
    1 Aug, 2017

Abstract

Transition from steady to oscillatory buoyancy convection of air in a laterally heated cubic box is studied numerically by straight-forward time integration of Boussinesq equations using a series of gradually refined finite volume grids. Horizontal and spanwise cube boundaries are assumed to be either perfectly thermally conducting or perfectly thermally insulated, which results in four different sets of thermal boundary conditions. Critical Grashof numbers are obtained by interpolation of numerically extracted growth/decay rates of oscillation amplitude to zero. Slightly supercritical flow regimes are described by time-averaged flows, snapshots, and spatial distribution of the oscillation amplitude. Possible similarities and dissimilarities with two-dimensional instabilities in laterally heated square cavities are discussed. Break of symmetries and sub- or supercritical character of bifurcations are examined. Three consequent transitions from steady to the oscillatory regime, from the oscillatory to the steady regime, and finally to the oscillatory flow, are found in the case of perfectly insulated horizontal and spanwise boundaries. Arguments for grid and time-step independence of the results are given.

► De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
    1 Aug, 2017

Abstract

The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD’s first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD’s performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD.

► Formation and behavior of counter-rotating vortex rings
    1 Aug, 2017

Abstract

Concentric, counter-rotating vortex ring formation by transient jet ejection between concentric cylinders was studied numerically to determine the effects of cylinder gap ratio, \(\frac{\Delta R}{R}\) , and jet stroke length-to-gap ratio, \(\frac{L}{\Delta R}\) , on the evolution of the vorticity and the trajectories of the resulting axisymmetric vortex pair. The flow was simulated at a jet Reynolds number of 1000 (based on \(\Delta R\) and the jet velocity), \(\frac{L}{\Delta R} \) in the range 1–20, and \(\frac{\Delta R}{R}\) in the range 0.05–0.25. Five characteristic flow evolution patterns were observed and classified based on \(\frac{L}{\Delta R} \) and \(\frac{\Delta R}{R}\) . The results showed that the relative position, relative strength, and radii of the vortex rings during and soon after formation played a prominent role in the evolution of the trajectories of their vorticity centroids at the later time. The conditions on relative strength of the vortices necessary for them to travel together as a pair following formation were studied, and factors affecting differences in vortex circulation following formation were investigated. In addition to the characteristics of the primary vortices, the stopping vortices had a strong influence on the initial vortex configuration and effected the long-time flow evolution at low \(\frac{L}{\Delta R}\) and small \(\frac{\Delta R}{R}\) . For long \(\frac{L}{\Delta R} \) and small \(\frac{\Delta R}{R}\) , shedding of vorticity was sometimes observed and this shedding was related to the Kelvin–Benjamin variational principle of maximal energy for steadily translating vortex rings.

► Effects of deformability of RBCs on their dynamics and blood flow passing through a stenosed microvessel: an immersed boundary-lattice Boltzmann approach
  13 Jul, 2017

Abstract

In this paper, the motion of high deformable (healthy) and low deformable (sick) red blood cells in a microvessel with and without stenosis is simulated using a combined lattice Boltzmann-immersed boundary method. The RBC is considered as neo-Hookean elastic membrane with bending resistance. The motion and deformation of the RBC under different values of the Reynolds number are evaluated. In addition, the variations of blood flow resistance and time-averaged pressure due to the motion and deformation of the RBC are assessed. It was found that a healthy RBC moves faster than a sick one. The apparent viscosity and blood flow resistance are greater for the case involving the sick RBC. Blood pressure at the presence of stenosis and low deformable RBC increases, which is thought of as the reason of many serious diseases including cardiovascular diseases. As the Re number increases, the RBC deforms further and moves easier and faster through the stenosis. The results of this study were compared to the available experimental and numerical results, and good agreements were observed.

► Effect of viscosity ratio on the motion of drops flowing on an inclined surface
  28 Jun, 2017

Abstract

The flow of two-dimensional drops on an inclined channel is studied by numerical simulations at finite Reynolds numbers. The effect of viscosity ratio on the behaviour of the two-phase medium is examined. The flow is driven by the acceleration due to gravity, and there is no pressure gradient along the flow direction. An implicit version of the finite difference/front-tracking method was developed and used in the present study. The lateral migration of a drop is studied first. It is found that the equilibrium position of a drop moves away from the channel floor as the viscosity ratio increases. However, the trend reverses beyond a certain viscosity ratio. Simulations with 40 drops in a relatively large channel show that there exists a limiting viscosity ratio where the drops behave like solid particles, and the effect of internal circulation of drops becomes negligible. This limiting condition resembles the granular flow regime except that the effect of interstitial fluid is present. The limiting viscosity ratio depends on the flow conditions (80 for \(Re=10\) , and 200 for \(Re=20\) ). There are two peaks in the areal fraction distribution of drops across the channel which is different from granular flow regime. It is also found that the peak in areal fraction distribution of drops moves away from the channel floor as the inclination angle of the channel increases.

► Iterative control of Görtler vortices via local wall deformations
  26 Jun, 2017

Abstract

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.


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