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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

► Evaluation of a 3D unstructured-mesh finite element model for dam-break floods
  16 Dec, 2017
Publication date: 4 January 2018
Source:Computers & Fluids, Volume 160
Author(s): Ting Zhang, Ling Peng, Ping Feng
This paper aims to comprehensively understand a 3D model for simulating dam-break floods through three test cases. The advantages and characteristics of this model are evaluated from different perspectives. Firstly, vertical inertial is considered in the 3D model. In the existing 1D and 2D flooding models, vertical inertia is usually ignored, resulting in unreliable results in high vertical inertia situations. A circular dam break case was designed and widely used for testing 2D models. Here it has been adopted to test the 3D model. Evident difference has been observed when compared with 2D modelling results. In order to reduce the vertical inertial in this case, we scaled the vertical size by 1:100, while kept the original horizontal size, then amplified the results according to the Froude number scaling rule. The results of the scaled model is very close to 2D modelling results. Therefore, the difference between the 3D and 2D modelling results are mainly caused by the vertical inertia. Thus it can be seen that 3D modelling techniques are needed when vertical inertia is not negligible. Secondly, the use of unstructured mesh makes this model more powerful in operating with complex topography, which is very important in real-world application. Five similar cases with different topography demonstrated that the complexity of topography affects the numerical solution process directly. However, this 3D model has powerful ability in utilizing very complex terrain. Thirdly, sensitivity of the model to the thickness of the artificial thin layer in dry areas (d0) and mesh resolution (Δx) have been analysed with a realistic dike-break flooding case. Smaller d0 produces more realistic results but costs more computational time. The model is more sensitive to mesh resolution when the terrain is more complex. Therefore, a multi-scale mesh with high-resolution in areas with complex terrain and low-resolution in flat regions is a good choice for this model. Also, trade-offs between modelling precision and efficiency should be considered when choosing a proper value of d0 and mesh resolution.

► A numerical investigation of matrix-free implicit time-stepping methods for large CFD simulations
  16 Dec, 2017
Publication date: 15 December 2017
Source:Computers & Fluids, Volume 159
Author(s): Arash Sarshar, Paul Tranquilli, Brent Pickering, Andrew McCall, Christopher J. Roy, Adrian Sandu
This paper is concerned with development and testing of advanced time-stepping methods for large unsteady CFD problems in the method of lines approach, where the semi-discretization in space is performed first. The performance of several time discretization methods is studied numerically with regards to computational efficiency, order of accuracy, and stability, as well as the ability to effectively treat stiff problems. We consider matrix-free implementations, a popular approach for time-stepping methods applied to large CFD applications due to its adherence to scalable matrix-vector operations and a small memory footprint. We compare explicit methods with matrix-free implementations of implicit, linearly-implicit, as well as Rosenbrock–Krylov methods. We show that Rosenbrock–Krylov methods are competitive with existing techniques excelling for a number of problem types and settings.

► A minimally-dissipative low-Mach number solver for complex reacting flows in OpenFOAM
  16 Dec, 2017
Publication date: 30 January 2018
Source:Computers & Fluids, Volume 162
Author(s): Malik Hassanaly, Heeseok Koo, Christopher F. Lietz, Shao Teng Chong, Venkat Raman
Large eddy simulation (LES) has become the de-facto computational tool for modeling complex reacting flows, especially in gas turbine applications. However, readily usable general-purpose LES codes for complex geometries are typically academic or proprietary/commercial in nature. The objective of this work is to develop and disseminate an open source LES tool for low-Mach number turbulent combustion using the OpenFOAM framework. In particular, a collocated-mesh approach suited for unstructured grid formulation is provided. Unlike other fluid dynamics models, LES accuracy is intricately linked to so-called primary and secondary conservation properties of the numerical discretization schemes. This implies that although the solver only evolves equations for mass, momentum, and energy, the implied discrete equation for kinetic energy (square of velocity) should be minimally-dissipative. Here, a specific spatial and temporal discretization is imposed such that this kinetic energy dissipation is minimized. The method is demonstrated using manufactured solutions approach on regular and skewed meshes for a canonical flow and a lab-scale turbulent flow problem.

► An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows
  16 Dec, 2017
Publication date: 4 January 2018
Source:Computers & Fluids, Volume 160
Author(s): L.M. Yang, C. Shu, W.M. Yang, Y. Wang, C.B. Lee
In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5.

► Numerical simulation of turbulent spots generated by unstable wave packets in a hypersonic boundary layer
  16 Dec, 2017
Publication date: 30 January 2018
Source:Computers & Fluids, Volume 162
Author(s): Pavel V. Chuvakhov, Alexander V. Fedorov, Anton O. Obraz
The generation of a turbulent spot by an unstable wave packet propagating in a Mach-6 flat-plate boundary layer is considered. The asymptotic shape of the wave packet is obtained in the far field from the excitation point using linear stability theory. Unsteady boundary conditions are formulated for direct numerical simulation. They allow for excitation of a well-developed wave packet with specified amplitude, skipping the linear growth stage. Robustness of these boundary conditions for modeling of the nonlinear breakdown of unstable wave packets into turbulent spots is examined.

► A stability analysis of the compressible boundary layer flow over indented surfaces
  16 Dec, 2017
Publication date: 4 January 2018
Source:Computers & Fluids, Volume 160
Author(s): Jesús Garicano-Mena, Esteban Ferrer, Silvia Sanvido, Eusebio Valero
This contribution presents a stability analysis for compressible boundary layer flows over indented surfaces. Specifically, the effects of increasing depth D/δ* and Ma number on perturbation time-decay rates and spatial amplification factors are quantified and compared with those of an unindented configuration.The indented surfaces represent aeronautical lifting surfaces endowed with the smooth gap resulting when a filler material applied at the junction of leading-edge and wing-box components retracts upon its curing process. Since the configuration considered is such that the parallel/weakly-parallel assumptions are necessarily compromised, a global temporal stability analysis is considered in this study. Our analysis does not require a parallel flow constrain, and hence it is believed to be valid when two dimensional effects are relevant.We find that small surface modifications enhance certain flow instabilities. An increase in Ma enhances further this behaviour: for the D/δ*=1.5,Ma=0.5 case, amplification factors at a given location can be up to 20 times larger than those corresponding to the unindented case.

► An improved divergence-free-condition compensated method for solving incompressible flows on collocated grids
  16 Dec, 2017
Publication date: 30 January 2018
Source:Computers & Fluids, Volume 162
Author(s): Pao-Hsiung Chiu
A collocated incompressible Navier–Stokes equations solver, which is based on an improved version of the divergence-free-condition compensated (DFC) method, is proposed in this paper. In order to avoid the difficulty and complexity of calculating the DFC source terms, an alternative procedure is proposed. In the present paper, the newly proposed IDFC source terms are derived through the following two steps: (1) solve the momentum equation on the cell-face in an approximated sense; (2) solve the momentum equation on the cell-center using the corresponding equations obtained from step (1). By this consistent treatment, the present method can avoid the odd-even decoupling problem, as well as the time-step-size dependent problem. For the sake of calculating a dispersively accurate spatial solution, the advection terms are approximated by the finite-volume-based dispersion-relation-preserving (DRP) advection scheme. Several benchmark problems with analytic solutions are investigated and compared with the present results, to show the applicability and accuracy of the present solver.

► A global particular solution meshless approach for the four-sided lid-driven cavity flow problem in the presence of magnetic fields
  16 Dec, 2017
Publication date: 4 January 2018
Source:Computers & Fluids, Volume 160
Author(s): J.M. Granados, H. Power, C.A. Bustamante, W.F. Flórez, A.F. Hill
The global meshless method of approximate Stokes particular solutions (MASPS) is used to solve a two-dimensional incompressible fluid flow in the presence of a uniform magnetic field, i.e. the Navier–Stokes equations with the Lorentz force as a source term in the momentum equations. Magnetohydrodynamic (MHD) problems at low magnetic Reynolds number (Rem) but finite flow Reynolds number (Re) are considered, so the fluid flow is affected by the magnetic field which remains unaltered by the fluid flow. The base functions to approximate the variables of the problem are the particular solutions of an auxiliary Stokes flow field in which a multiquadric (MQ) radial basis function (RBF) is applied as source term. The nonlinear equations resulting from the discretization in a fully implicit finite-difference form are solved by a variable step Newton–Raphson method. The capability of the numerical scheme to simulate MHD problems for different geometries is shown by solving the one-sided lid-driven cavity and the backward facing step flows in the presence of horizontal and vertical magnetic fields, respectively. The existence of simultaneous steady-state solutions in the four-sided lid-driven cavity (4S-LDC) problem is studied with the MASPS for Re between 0 and 1000 and Hartmann numbers (Ha) up to 10. Critical Reynolds numbers (Rec), corresponding to stationary and Hopf bifurcations, are evidenced. Bifurcation diagrams are constructed based on simultaneous solutions and their stability analyses. The increase of Ha modifies the bifurcation diagram and causes the displacement of bifurcation points towards higher Re. Three types of bifurcation, detected by the MASPS in the 4S-LDC flow, are classified based on the stability state analyses. Vertical and oblique magnetic fields are imposed on the flow to study their influence on the bifurcation maps. The effects of the vertical magnetic field on the map are stronger than those of the oblique field.

► High-order linearly implicit two-step peer schemes for the discontinuous Galerkin solution of the incompressible Navier–Stokes equations
  16 Dec, 2017
Publication date: 30 January 2018
Source:Computers & Fluids, Volume 162
Author(s): F.C. Massa, G. Noventa, M. Lorini, F. Bassi, A. Ghidoni
In this work the use of high-order linearly implicit Rosenbrock-type two-step peer schemes has been investigated to integrate in time the high-order discontinuous Galerkin space discretization of the incompressible Navier–Stokes equations.The aim of the present paper is (i) to describe the implementation of the schemes in the DG code MIGALE with focus on the computation of the set of the coefficients and the starting procedure, (ii) to describe the coupling of the scheme with an adaptive time-step strategy in order to investigate its effect on the robustness and computational efficiency of the simulations, and (iii) to provide some practical informations regarding the choice of the “optimal” time integration for LES and DNS on the basis of the requested accuracy. Peer schemes, up to sixth order, have been considered and compared with traditional one-step linearly implicit Rosenbrock, up to fifth order, and ESDIRK, up to fourth order, schemes available in literature in terms of accuracy and computational efficiency. For the sake of completeness, the sets of coefficients of the schemes here considered have been reported in an appendix.The reliability, robustness and accuracy of the proposed implementation have been assessed by computing the Prothero–Robinson example, the laminar travelling waves solution on a doubly periodic unit square domain and the laminar flow around a circular cylinder for a Reynolds number Re=100. Travelling waves and cylinder testcases have been also modified to investigate the behaviour of the schemes with time-dependent boundary conditions. In the former case replacing periodic boundary conditions with given boundary condition based on the analytical solution, while in the latter case considering a rotating cylinder.

► Hybrid monotonicity-preserving piecewise parabolic method for compressible Euler equations
  16 Dec, 2017
Publication date: 15 December 2017
Source:Computers & Fluids, Volume 159
Author(s): Yaqun Yu, Baolin Tian, Zeyao Mo
In this article, we present a high-accuracy high-resolution hybrid scheme with strong robustness for solutions of compressible Euler equations, particularly those relating to strong discontinuity. The fifth-order monotonicity-preserving (MP5) scheme of Suresh and Huynh has high accuracy; however, its robustness is relatively weak. To improve the robustness and resolution, the MP5 scheme is conjugated with a fourth-order piecewise parabolic method (PPM) in a complementary approach. An adaptive constraint is used to detect which scheme is applied at the current position to guarantee the strong robustness and high accuracy. Through numerical experiments, our hybrid scheme demonstrates a stronger robustness and higher resolution than the traditional scheme and the hybrid scheme MP5-R by He without loss of accuracy.

International Journal of Computational Fluid Dynamics top

► Lattice Boltzmann simulation of multiple droplets impingement and coalescence in an inkjet-printed line patterning process
  27 Nov, 2017
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► Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh
  13 Nov, 2017
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► Portable implementation model for CFD simulations. Application to hybrid CPU/GPU supercomputers
  27 Oct, 2017
Volume 31, Issue 9, November 2017, Page 396-411
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► A study on the behaviour of high-order flux reconstruction method with different low-dissipation numerical fluxes for large eddy simulation
  19 Oct, 2017
Volume 31, Issue 9, November 2017, Page 339-361
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► High-resolution multi-code implementation of unsteady Navier–Stokes flow solver based on paralleled overset adaptive mesh refinement and high-order low-dissipation hybrid schemes
  19 Oct, 2017
Volume 31, Issue 9, November 2017, Page 379-395
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► A new high-accuracy scheme for compressible turbulent flows
  22 Aug, 2017
Volume 31, Issue 9, November 2017, Page 362-378
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► Erratum
  18 Aug, 2014
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International Journal for Numerical Methods in Fluids top

► Numerical bifurcation analysis for 3-dimensional sudden expansion fluid dynamic problem
  13 Dec, 2017

Summary

This paper deals with bifurcation analysis methods based on the asymptotic-numerical method. It is used to investigate 3-dimensional (3D) instabilities in a sudden expansion. To do so, high-performance computing is implemented in ELMER, ie, an open-source multiphysical software. In this work, velocity-pressure mixed vectors are used with asymptotic-numerical method–based methods, remarks are made for the branch-switching method in the case of symmetry-breaking bifurcation, and new 3D instability results are presented for the sudden expansion ratio, ie, E=3. Critical Reynolds numbers for primary bifurcations are studied with the evolution of a geometric parameter. New values are computed, which reveal new trends that complete a previous work. Several kinds of bifurcation are depicted and tracked with the evolution of the spanwise aspect ratio. One of these relies on a fully 3D effect as it breaks both spanwise and top-bottom symmetries. This bifurcation is found for smaller aspect ratios than expected. Furthermore, a critical Reynolds number is found for the aspect ratio, ie, Ai=1, which was not previously reported. Finally, primary and secondary bifurcations are efficiently detected and all post-bifurcated branches are followed. This makes it possible to plot a complete bifurcation diagram for this 3D case.

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This paper deals with bifurcation analysis methods based on the Asymptotic Numerical Method. Remarks are made for the branch-switching method in the case of symmetry-breaking bifurcation and new three-dimensional instabilities results are presented for the sudden expansion ratio E=3. Critical Reynolds numbers for primary bifurcations are studied and several kinds of bifurcation are depicted and tracked with the evolution of the span-wise aspect ratio, moreover primary and secondary bifurcations are efficiently detected and all post-bifurcated branches are followed.

► Issue Information
  12 Dec, 2017

No abstract is available for this article.

► The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical hankel shape functions
  12 Dec, 2017

Summary

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating two-dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier–Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kind of Bessel functions. In addition, these functions have properties such as piecewise continuity, and etc. For enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. Also, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, four benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.

► A sharp-interface immersed boundary framework for simulations of high-speed inviscid compressible flows
  11 Dec, 2017

Summary

A new finite-volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high-speed inviscid compressible flows. The IB method adopts a sharp-interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid-fluid interface. We show that proposed reconstruction leads to second-order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift-off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape-changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.

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A new sharp-interface immersed boundary method based on inverse-distance weighting reconstruction is proposed for high-speed compressible flows. The discrete conservation errors from the approach are shown to be finite but diminishing with grid refinement. The solver is applied to several flow problems in supersonic and hypersonic flows including shape optimisation and demonstrates the efficacy of the methodology.

► On the use of the continuous adjoint method to compute nongeometric sensitivities
    6 Dec, 2017

Summary

This work explores an alternative approach to computing sensitivity derivatives of functionals, with respect to a broader range of control parameters. It builds upon the complementary character of Riemann problems that describe the Euler flow and adjoint solutions. In a previous work, we have discussed a treatment of the adjoint boundary problem, which made use of such complementarity as a means to ensure well-posedness. Here, we show that the very same adjoint solution that satisfies those boundary conditions also conveys information on other types of sensitivities. In essence, then, that formulation of the boundary problem can extend the range of applications of the adjoint method to a host of new possibilities.

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This work presents a novel application of the General Theory of Sensitivity Analysis, as developed by D.G. Cacuci, to Euler compressible flows. It adopts the continuous form of the adjoint method and addresses both physical and adjoint boundary conditions in terms of complete and complementary Riemann problems. This approach enables one to compute sensitivity derivatives other than those related to geometry optimization, with respect to a large variety of objective functionals.

► Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space
    4 Dec, 2017

Summary

In a previous paper, the authors presented an elemental enriched space to be used in a finite-element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier-Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite-element code is extremely easy with the version presented here because the new shape functions are based on the usual finite-element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.

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An Elemental Enriched Space capable to reproduces kinks and jumps in the velocity and pressure field on internal interfaces which does not match with the Finite Element mesh is presented. The enriched space, which mitigates the lack of continuity required by the weak form, is evaluated for incompressible and two-phase fluid mechanic problems. The condensing strategy employed does not change either: the total number of degree of freedom nor the matrix graph, leading to a significant computer time reduction, mainly when internal interfaces move though a fixed FE mesh.

► Depth-integrated non-hydrostatic free-surface flow modelling using weighted-averaged equations
  28 Nov, 2017

Summary

SUMMARY

In this study, a depth-integrated non-hydrostatic flow model is developed using the method of weighted residuals. Using a unit weighting function depth-integrated Reynolds-Averaged Navier-Stokes (RANS) equations are obtained. Prescribing polynomial variations for the field variables in the vertical direction, a set of perturbation parameters remains undetermined. The model is closed generating a set of weighted averaged equations using a suitable weighting function. The resulting depth-integrated, non-hydrostatic model is solved with a semi-implicit finite-volume finite-difference scheme. The explicit part of the model is a Godunov-type finite volume scheme that uses the HLLC approximate Riemann solver to determine the non-hydrostatic depth-averaged velocity field. The implicit part of the model is solved using a Newton–Raphson algorithm to incorporate the effects of the pressure field in the solution. The model is applied with good results to a set of problems of coastal and river engineering, including steady flow over fixed bed-forms, solitary wave propagation, solitary wave run-up, linear frequency dispersion, propagation of sinusoidal waves over a submerged bar and dam-break flood waves.

► Novel local smoothness indicators for improving the third-order WENO scheme
  28 Nov, 2017

Summary

The local smoothness indicators play an important role in the performance of a weighted essentially non-oscillatory (WENO) scheme. Due to having only two points available on each sub-stencil, the local smoothness indicators calculated by conventional methods of Jiang and Shu [1] make the third-order WENO scheme too dissipative. In this paper, we propose a different method to calculate the indicators by using all the three points on the global stencil of the third-order WENO scheme. The numerical results demonstrate that the WENO scheme with the new indicators has less dissipation and better resolution than the ones of Jiang and Shu's for both smooth and discontinuous solutions.

► Anisotropic adaptive stabilized finite element solver for RANS models
  23 Nov, 2017

Summary

Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge-based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A variational multiscale-stabilized finite element method is used to solve the incompressible Navier-Stokes equations. Finally, the Spalart-Allmaras turbulence model is solved using the streamline upwind Petrov-Galerkin method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases.

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In this paper, we propose an adaptive anisotropic mesh methodology for performing accurate numerical simulations of turbulent flows past complex geometries. It couples a stabilized variational multiscale Navier-Stokes modified solver to account for high stretched elements, a Spalart-Allmaras turbulent model with a dynamic anisotropic mesh adaptation algorithm.

► Characteristic-based inlet and outlet boundary conditions for incompressible flows
  21 Nov, 2017

Summary

Determining boundary conditions (BCs) for incompressible flows is such a delicate matter that affects the accuracy of the results. In this research, a new characteristic-based BC for incompressible Navier-Stokes equations is introduced. Discretization of equations has been done via finite volume. Additionally, artificial compressibility correction has been employed to deal with equations. Ordinary extrapolation from inner cells of a domain was used as a traditional way to estimate pressure and velocities on solid wall and inlet/outlet boundaries. Here, this method was substituted by the newly proposed BCs based on the characteristics of artificial compressibility equations. To follow this purpose, a computer code has been developed to carry out series of numerical tests for a flow over a backward-facing step and was applied to a wide range of Reynolds numbers and grid combinations. Calculation of convective and viscous fluxes was done using Jameson's averaging scheme. Employing the characteristic-based method for determining BCs has shown an improved convergence rate and reduced calculation time comparing with those of traditional ones. Furthermore, with the reduction of domain and computational cells, a similar accuracy was achieved for the results in comparison with the ones obtained from the traditional extrapolation method, and these results were in good agreement with the ones in the literature.

Thumbnail image of graphical abstract

In this research, a new characteristics based boundary condition for incompressible Navier-Stokes equations is introduced. Employing the characteristic-based method for determining boundary conditions has shown an improved convergence rate and reduced calculation time comparing with those of traditional ones. Furthermore, with the reduction of domain and computational cells, a similar accuracy was achieved for the results in comparison with the ones obtained from the traditional extrapolation method and these results were in good agreement with the ones in the literature.

Journal of Computational Physics top

► A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Siwei Duo, Hans Werner van Wyk, Yanzhi Zhang
In this paper, we develop a novel finite difference method to discretize the fractional Laplacian (Δ)α/2 in hypersingular integral form. By introducing a splitting parameter, we formulate the fractional Laplacian as the weighted integral of a weak singular function, which is then approximated by the weighted trapezoidal rule. Compared to other existing methods, our method is more accurate and simpler to implement, and moreover it closely resembles the central difference scheme for the classical Laplace operator. We prove that for uC3,α/2(R), our method has an accuracy of O(h2)uniformly for anyα(0,2), while for uC1,α/2(R), the accuracy is O(h1α/2). The convergence behavior of our method is consistent with that of the central difference approximation of the classical Laplace operator. Additionally, we apply our method to solve the fractional Poisson equation and study the convergence of its numerical solutions. The extensive numerical examples that accompany our analysis verify our results, as well as give additional insights into the convergence behavior of our method.

► A numerical study of the 3-periodic wave solutions to KdV-type equations
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Yingnan Zhang, Xingbiao Hu, Jianqing Sun
In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg–de Vries equation, the Sawada–Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2+1)-dimensional Kadomtsev–Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

► An optimized hybrid Convolutional Perfectly Matched Layer for efficient absorption of electromagnetic waves
  16 Dec, 2017
Publication date: 1 March 2018
Source:Journal of Computational Physics, Volume 356
Author(s): Amirashkan Darvish, Bijan Zakeri, Nafiseh Radkani
A hybrid technique is studied in order to improve the performance of Convolutional Perfectly Matched Layer (CPML) in the Finite Difference Time Domain (FDTD) medium. This technique combines the first order of Higdon's annihilation equation as Absorbing Boundary Condition (ABC) with CPML to vanish the Perfect Electric Conductor (PEC) effects at the end of the CPML region. An optimization algorithm is required to find optimum parameters of the proposed absorber. In this investigation, the Particle Swarm Optimization (PSO) is utilized with two separate objective functions in order to minimize the average and peak value of relative error. Using a standard test, the overall performance of the proposed absorber is compared to the original CPML. The results clearly illustrate this method provides approximately 10 dB enhancements in CPML absorption error. The performance, memory and time requirement of the novel absorber, hybrid CPML (H-CPML), was analyzed during 2D and 3D tests and compared to most reported PMLs. The H-CPML requirement of computer resources is similar to CPML and can simply be implemented to truncate FDTD domains. Furthermore, an optimized set of parameters are provided to generalize the hybrid method.

► Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Daniele A. Di Pietro, Jérôme Droniou, Gianmarco Manzini
In this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart–Thomas–Nédélec subspace. We prove that the novel DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition.

► Gradient recovery for elliptic interface problem: III. Nitsche's method
  16 Dec, 2017
Publication date: 1 March 2018
Source:Journal of Computational Physics, Volume 356
Author(s): Hailong Guo, Xu Yang
This is the third paper on the study of gradient recovery for elliptic interface problems. In our previous works Guo and Yang (2017) [23], we developed gradient recovery methods for elliptic interface problems based on body-fitted meshes and immersed finite element methods. Despite the efficiency and accuracy that these methods bring to recover the gradient, there are still some cases in unfitted meshes where skinny triangles appear in the generated local body-fitted triangulations that destroy the accuracy of recovered gradient near the interface. In this paper, we propose a gradient recovery technique based on Nitsche's method for elliptic interface problems, which avoids the loss of accuracy of gradient near the interface caused by skinny triangles. We analyze the supercloseness between the gradient of the numerical solution by the Nitsche's method and the gradient of the interpolation of the exact solution, which leads to the superconvergence of the proposed gradient recovery method. We also present several numerical examples to validate the theoretical results.

► Fluid–structure interaction simulation of floating structures interacting with complex, large-scale ocean waves and atmospheric turbulence with application to floating offshore wind turbines
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Antoni Calderer, Xin Guo, Lian Shen, Fotis Sotiropoulos
We develop a numerical method for simulating coupled interactions of complex floating structures with large-scale ocean waves and atmospheric turbulence. We employ an efficient large-scale model to develop offshore wind and wave environmental conditions, which are then incorporated into a high resolution two-phase flow solver with fluid–structure interaction (FSI). The large-scale wind–wave interaction model is based on a two-fluid dynamically-coupled approach that employs a high-order spectral method for simulating the water motion and a viscous solver with undulatory boundaries for the air motion. The two-phase flow FSI solver is based on the level set method and is capable of simulating the coupled dynamic interaction of arbitrarily complex bodies with airflow and waves. The large-scale wave field solver is coupled with the near-field FSI solver with a one-way coupling approach by feeding into the latter waves via a pressure-forcing method combined with the level set method. We validate the model for both simple wave trains and three-dimensional directional waves and compare the results with experimental and theoretical solutions. Finally, we demonstrate the capabilities of the new computational framework by carrying out large-eddy simulation of a floating offshore wind turbine interacting with realistic ocean wind and waves.

► Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows
  16 Dec, 2017
Publication date: 1 March 2018
Source:Journal of Computational Physics, Volume 356
Author(s): Yukihito Suzuki
A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn–Hilliard and Allen–Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

► Asymptotic analysis for close evaluation of layer potentials
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Camille Carvalho, Shilpa Khatri, Arnold D. Kim
We study the evaluation of layer potentials close to the domain boundary. Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in nano-optics. When numerically evaluating layer potentials, it is natural to use the same quadrature rule as the one used in the Nyström method to solve the underlying boundary integral equation. However, this method is problematic for evaluation points close to boundaries. For a fixed number of quadrature points, N, this method incurs O(1) errors in a boundary layer of thickness O(1/N). Using an asymptotic expansion for the kernel of the layer potential, we remove this O(1) error. We demonstrate the effectiveness of this method for interior and exterior problems for Laplace's equation in two dimensions.

► Multithreaded implicitly dealiased convolutions
  16 Dec, 2017
Publication date: 1 March 2018
Source:Journal of Computational Physics, Volume 356
Author(s): Malcolm Roberts, John C. Bowman
Implicit dealiasing is a method for computing in-place linear convolutions via fast Fourier transforms that decouples work memory from input data. It offers easier memory management and, for long one-dimensional input sequences, greater efficiency than conventional zero-padding. Furthermore, for convolutions of multidimensional data, the segregation of data and work buffers can be exploited to reduce memory usage and execution time significantly. This is accomplished by processing and discarding data as it is generated, allowing work memory to be reused, for greater data locality and performance. A multithreaded implementation of implicit dealiasing that accepts an arbitrary number of input and output vectors and a general multiplication operator is presented, along with an improved one-dimensional Hermitian convolution that avoids the loop dependency inherent in previous work. An alternate data format that can accommodate a Nyquist mode and enhance cache efficiency is also proposed.

► Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids
  16 Dec, 2017
Publication date: 15 February 2018
Source:Journal of Computational Physics, Volume 355
Author(s): Euntaek Lee, Hyung Taek Ahn, Hong Luo
We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

Journal of Turbulence top

► A restricted nonlinear large eddy simulation model for high Reynolds number flows
  23 Nov, 2017
.
► Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence
  23 Nov, 2017
.
► Quasi-radial wall jets as a new concept in boundary layer flow control
    3 Nov, 2017
Volume 19, Issue 1, January 2018, Page 25-48
.
► The self-similarity of wall-bounded temporally accelerating turbulent flows
    3 Nov, 2017
Volume 19, Issue 1, January 2018, Page 49-60
.
► Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall
    3 Nov, 2017
Volume 19, Issue 1, January 2018, Page 72-105
.
► On the Kelvin–Helmholtz and von Kármán vortices in the near-wake of semicircular cylinders with flaps
    3 Nov, 2017
Volume 19, Issue 1, January 2018, Page 61-71
.
► Vortex dynamics of a trapezoidal bluff body placed inside a circular pipe
  15 Sep, 2017
Volume 19, Issue 1, January 2018, Page 1-24
.
► Passive control of the flow around unsteady aerofoils using a self-activated deployable flap
  13 Apr, 2017
.

Physics of Fluids top

► Analysis of electro-osmotic flow over a slightly bumpy plate
  15 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Jet formation of SF6 bubble induced by incident and reflected shock waves
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Wave-induced collisions of thin floating disks
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Development of vortex structures in the wake of a sharp-edged bluff body
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Resonances of Newtonian fluids in elastomeric microtubes
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► DEM study of the size-induced segregation dynamics of a ternary-size granular mixture in the rolling-regime rotating drum
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► The culmination of an inverse cascade: Mean flow and fluctuations
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Shapes and paths of an air bubble rising in quiescent liquids
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Experimental study on imbibition displacement mechanisms of two-phase fluid using micromodel: Fracture network, distribution of pore size, and matrix construction
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.
► Nonspherical sub-millimeter gas bubble oscillations: Parametric forcing and nonlinear shape mode coupling
  14 Dec, 2017
Physics of Fluids, Volume 29, Issue 12, December 2017.

Theoretical and Computational Fluid Dynamics top

► Artificial eigenmodes in truncated flow domains
  14 Dec, 2017

Abstract

Whenever linear eigenmodes of open flows are computed on a numerical domain that is truncated in the streamwise direction, artificial boundary conditions may give rise to spurious pressure signals that are capable of providing unwanted perturbation feedback to upstream locations. The manifestation of such feedback in the eigenmode spectrum is analysed here for two simple configurations. First, explicitly prescribed feedback in a Ginzburg–Landau model is shown to produce a spurious eigenmode branch, named the ‘arc branch’, that strongly resembles a characteristic family of eigenmodes typically present in open shear flow calculations. Second, corresponding mode branches in the global spectrum of an incompressible parallel jet in a truncated domain are examined. It is demonstrated that these eigenmodes of the numerical model depend on the presence of spurious forcing of a local \(k^+\) instability wave at the inflow, caused by pressure signals that appear to be generated at the outflow. Multiple local \(k^+\) branches result in multiple global eigenmode branches. For the particular boundary treatment chosen here, the strength of the pressure feedback from the outflow towards the inflow boundary is found to decay with the cube of the numerical domain length. It is concluded that arc branch eigenmodes are artefacts of domain truncation, with limited value for physical analysis. It is demonstrated, for the example of a non-parallel jet, how spurious feedback may be reduced by an absorbing layer near the outflow boundary.

► Stochastic growth of cloud droplets by collisions during settling
  11 Dec, 2017

Abstract

In the last stage of droplet growth in clouds which leads to drizzle formation, larger droplets begin to settle under gravity and collide and coalesce with smaller droplets in their path. In this article, we shall deal with the simplified problem of a large drop settling amidst a population of identical smaller droplets. We present an expression for the probability that a given large drop suffers a given number of collisions, for a general statistically homogeneous distribution of droplets. We hope that our approach will serve as a valuable tool in dealing with droplet distribution in real clouds, which has been found to deviate from the idealized Poisson distribution due to mechanisms such as inertial clustering.

► Effective particle size from molecular dynamics simulations in fluids
    8 Dec, 2017

Abstract

We report molecular dynamics simulations designed to investigate the effective size of colloidal particles suspended in a fluid in the vicinity of a rigid wall where all interactions are defined by smooth atomic potential functions. These simulations are used to assess how the behavior of this system at the atomistic length scale compares to continuum mechanics models. In order to determine the effective size of the particles, we calculate the solvent forces on spherical particles of different radii as a function of different positions near and overlapping with the atomistically defined wall and compare them to continuum models. This procedure also then determines the effective position of the wall. Our analysis is based solely on forces that the particles sense, ensuring self-consistency of the method. The simulations were carried out using both Weeks–Chandler–Andersen and modified Lennard-Jones (LJ) potentials to identify the different contributions of simple repulsion and van der Waals attractive forces. Upon correction for behavior arising the discreteness of the atomic system, the underlying continuum physics analysis appeared to be correct down to much less than the particle radius. For both particle types, the effective radius was found to be \(\sim 0.75\sigma \) , where \(\sigma \) defines the length scale of the force interaction (the LJ diameter). The effective “hydrodynamic” radii determined by this means are distinct from commonly assumed values of \(0.5\sigma \) and \(1.0\sigma \) , but agree with a value developed from the atomistic analysis of the viscosity of such systems.

► Effects of geometric modulation and surface potential heterogeneity on electrokinetic flow and solute transport in a microchannel
    7 Dec, 2017

Abstract

A numerical investigation is performed on the electroosmotic flow (EOF) in a surface-modulated microchannel to induce enhanced solute mixing. The channel wall is modulated by placing surface-mounted obstacles of trigonometric shape along which the surface potential is considered to be different from the surface potential of the homogeneous part of the wall. The characteristics of the electrokinetic flow are governed by the Laplace equation for the distribution of external electric potential; the Poisson equation for the distribution of induced electric potential; the Nernst–Planck equations for the distribution of ions; and the Navier–Stokes equations for fluid flow simultaneously. These nonlinear coupled set of governing equations are solved numerically by a control volume method over the staggered system. The influence of the geometric modulation of the surface, surface potential heterogeneity and the bulk ionic concentration on the EOF is analyzed. Vortical flow develops near a surface modulation, and it becomes stronger when the surface potential of the modulated region is in opposite sign to the surface potential of the homogeneous part of the channel walls. Vortical flow also depends on the Debye length when the Debye length is in the order of the channel height. Pressure drop along the channel length is higher for a ribbed wall channel compared to the grooved wall case. The pressure drop decreases with the increase in the amplitude for a grooved channel, but increases for a ribbed channel. The mixing index is quantified through the standard deviation of the solute distribution. Our results show that mixing index is higher for the ribbed channel compared to the grooved channel with heterogeneous surface potential. The increase in potential heterogeneity in the modulated region also increases the mixing index in both grooved and ribbed channels. However, the mixing performance, which is the ratio of the mixing index to pressure drop, reduces with the rise in the surface potential heterogeneity.

► Control of a three-dimensional turbulent shear layer by means of oblique vortices
    2 Dec, 2017

Abstract

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of \(40^\circ \) . Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than \(50^\circ \) from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress \(-\rho \overline{u'v'}\) . The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.

► Cluster-based control of a separating flow over a smoothly contoured ramp
    1 Dec, 2017

Abstract

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin–Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

► Spanwise effects on instabilities of compressible flow over a long rectangular cavity
    1 Dec, 2017

Abstract

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\) . In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\) . To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\) , in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.

► Linear instability in the wake of an elliptic wing
    1 Dec, 2017

Abstract

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of \(Re_{c}=1750\) and two angles of attack, \(\mathrm{{AoA}}=0^\circ \) and \(5^\circ \) . Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

► Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers
    1 Dec, 2017

Abstract

Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases shows that they enable convergence toward solutions that are unstable to stationary and oscillatory disturbances, with either a single or multiple frequency content. Finally, comparisons with SFD are also performed, showing significant reduction in computer cost for complex flows by using the implicit multi-step MGM schemes.

► Reducing the pressure drag of a D-shaped bluff body using linear feedback control
    1 Dec, 2017

Abstract

The pressure drag of blunt bluff bodies is highly relevant in many practical applications, including to the aerodynamic drag of road vehicles. This paper presents theory revealing that a mean drag reduction can be achieved by manipulating wake flow fluctuations. A linear feedback control strategy then exploits this idea, targeting attenuation of the spatially integrated base (back face) pressure fluctuations. Large-eddy simulations of the flow over a D-shaped blunt bluff body are used as a test-bed for this control strategy. The flow response to synthetic jet actuation is characterised using system identification, and controller design is via shaping of the frequency response to achieve fluctuation attenuation. The designed controller successfully attenuates integrated base pressure fluctuations, increasing the time-averaged pressure on the body base by 38%. The effect on the flow field is to push the roll-up of vortices further downstream and increase the extent of the recirculation bubble. This control approach uses only body-mounted sensing/actuation and input–output model identification, meaning that it could be applied experimentally.


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