Simulation Of Compressible Turbulent Flows Research Articles

Compact high-order gas-kinetic scheme for direct numerical simulation of compressible turbulent flows

In this paper, the three-dimensional fully compact high-order gas-kinetic scheme (HGKS) is proposed for the direct numerical simulation of compressible turbulent flows. Because of the high-order gas evolution model, the numerical fluxes as well as the point-wise conservative variables can be evaluated from the time-accurate gas distribution function at the cell interface. As a result, both the cell-averaged variables and their cell-averaged gradients can be updated inside each cell. Based on the cell averaged values and their gradients, the compact Hermite weighted essentially non-oscillatory (HWENO) scheme is developed, in which the dimension-by-dimension reconstruction is used for three-dimensional turbulences. In both normal and tangential directions, the fifth-order HWENO reconstruction is adopted. Compared with the classical WENO scheme, the stencil for the HWENO scheme only contains 33 cells for each cell. To achieve the temporal accuracy, the two-stage fourth-order temporal discretization is used. For the evaluation of point-wise variables, the simplified third-order gas-kinetic solver is used. Several classical benchmark problems are simulated, which validate the accuracy, resolution, and robustness of compact HGKS. As a comparison, the numerical results of HGKS using non-compact WENO reconstruction are also provided. Due to the compact stencil, the compact HGKS has a favorable performance for turbulence simulation in resolving the multi-scale structures.

Kinetic-energy- and pressure-equilibrium-preserving schemes for real-gas turbulence in the transcritical regime

Numerical simulations of compressible turbulent flows governed by real-gas equations of state, such as high-pressure transcritical flows, are strongly susceptible to instabilities. In addition to the inherent multi-scale nature of the flow, the presence of a pseudo-interface can generate spurious pressure oscillations when conventional schemes are utilized. This study proposes a general framework to derive and analyze discretization methods that are able to preserve kinetic energy by convection, and simultaneously maintain pressure equilibrium in discontinuity-free compressible real-gas flows. The formal analysis reveals that the discrete pressure-equilibrium condition can be fulfilled at most to second-order accuracy, as it requires the spatial differential operator to satisfy a discrete chain rule when total or internal energy are directly discretized. A novel class of schemes based on the solution of a pressure equation is thus proposed, which preserves mass, momentum, kinetic energy and pressure equilibrium, but not total energy. Extensive numerical tests of increasing complexity confirm the theoretical predictions, and show that the proposed scheme is capable of providing non-dissipative, stable and oscillation-free simulations, unlike existing methods tailored for the transcritical regime.

A revised WENO‐THINC scheme for the general structured mesh and applications in the direct numerical simulation of compressible turbulent flows

AbstractThe Tangent of Hyperbola for INterface Capturing (THINC) scheme allows a jump‐like reconstruction and brings about a significant improvement in resolving the discontinuous part of the numerical solutions. However, it is found that the original THINC scheme loses accuracy when working on the stretched, curvilinear or highly‐skewed grid. In this study, we propose a simple strategy to determine the jump thickness parameter in the THINC function, so as to effectively suppress the unphysical oscillation. A Boundary Variation Diminishing (BVD) guideline is introduced to make options between the Weighted Essentially Non‐Oscillatory (WENO) scheme and the modified THINC scheme, thus both the smooth and discontinuous solutions can be reconstructed properly avoiding distortion of grids. Numerical validations indicate that the improved WENO‐THINC‐BVD approach maintains high resolution and is more robust on various types of non‐uniform meshes. The present method is further extended to validate the low‐dissipation property in resolving higher wave numbers portions by simulating an isotropic turbulence decay problem. Finally, we perform the direct numerical simulation (DNS) of a spatially evolving adiabatic flat plate boundary‐layer flow problem at a supersonic Mach number (). Numerical results show the predicted mean flow variables and the normalized shear stress agree well with the experimental data, significant improvements are found in the resolution of the small‐scale vortices, especially in the transition process.

Helical model based on artificial neural network for large eddy simulation of compressible wall-bounded turbulent flows

Similar to the kinetic energy cascade, a helicity cascade is also a basic and key process in the generation and evolution of the turbulent flows. Furthermore, the helicity flux (HF) plays a crucial role between two scales in the helicity cascade. In this study, we will supply a new helical model constrained by the helicity flux for the large eddy simulation of the compressible turbulent flows. Then, in order to obtain a more precise HF, the local coefficient of the modeled HF is determined by the artificial neural network (ANN) method. The new model combines merits of the high robustness and the correlation with the real turbulence. In the test case of the compressible turbulent channel flow, the new model can supply a more accurate mean velocity profile, turbulence intensities, Reynolds stress, etc. Then, for the test in the compressible flat-plate boundary layer, the new model can also precisely predict the onset and peak of the transition process, the skin-friction coefficient, the mean velocity in the turbulent region, etc. Moreover, the ANN here is a semi-implicit method, and the new model would be easier to be generalized to simulate other types of the compressible wall-bounded turbulent flows.

STREAmS-2.0: Supersonic turbulent accelerated Navier-Stokes solver version 2.0

We present STREAmS-2.0, an updated version of the flow solver STREAmS, first introduced in Bernardini et al. (2021) [1]. STREAmS-2.0 has an object-oriented design which separates the physics equations from the specific back-end, making the code more suitable for future expansions, such as porting to novel computing architectures or implementation of additional flow physics. Similarly to the previous version, STREAmS-2.0 supports NVIDIA-GPU and CPU back-ends. Additionally, this version features improvements of the input/output data management, new energy and entropy preserving schemes for the discretization of the convective fluxes, recycling/rescaling inflow boundary condition, and a model for thermally perfect gases with variable specific heats. New version program summaryProgram Title: STREAmSCPC Library link to program files:https://doi.org/10.17632/hdcgjpzr3y.2Developer's repository link:https://github.com/STREAmS-CFD/STREAmS-2Licensing provisions: GPLv3Programming language: Fortran, CUDAJournal reference of previous version: M. Bernardini, D. Modesti, F. Salvadore, and S. Pirozzoli. STREAmS: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows. Comput. Phys. Commun. 263 (2021) 107906.Does the new version supersede the previous version?: Yes.Reasons for the new version: New code structure and release of new features.Summary of revisions:•The original solver [1] has been rewritten following an object-oriented design implemented through Fortran derived types that include variables and type bound procedures. The new software architecture has been designed to increase modularity and extensibility of the code, allowing users to add new back-ends and physics equations while maintaining the same code structure. This allows users to reuse portions of the code that are independent of the physics equations, the back-end, or both. The layer of computing procedures maintains a lean structure that can be highly optimized with respect to the implemented back-end.•Input handling is now based on the classic .ini format improving both user readability and input data management.•A family of new kinetic energy and entropy preserving schemes (KEEP) are now available and can be selected for stable, non-dissipative and accurate spatial discretization of the convective terms of the Navier–Stokes equations in smooth flow regions [2]. Concerning the shock-capturing flux, the improved low-dissipative WENO-Z scheme proposed by [3] is now available.•New inflow boundary conditions based on the recycling/rescale approach [4] have been implemented for the simulation of spatially evolving compressible turbulent boundary layers. Moreover, a new inflow condition based on the solution of the compressible Blasius equation is available to take into account the case of laminar boundary layers.•The constitutive relations have been generalized to take into account thermally perfect gases with variable specific heats, approximated with polynomial functions of the temperature that can be specified by the user [5].•A new stretching function has been implemented to improve the distribution of grid nodes for the computation of wall-bounded turbulent flows. The formulation blends uniform near-wall spacing with uniform resolution in terms of Kolmogorov units in the outer wall layer, guaranteeing accuracy with higher computational efficiency [6].Nature of problem: The code solves the compressible Navier–Stokes equations in Cartesian coordinates for a thermally perfect gas. The solver is designed for direct numerical simulation (DNS) of compressible supersonic turbulent boundary layers and various canonical configurations are supported, including turbulent channel flow, laminar and turbulent boundary layer and shock-wave/boundary layer interaction.Solution method: The equations are discretized using high-order finite difference approximations with hybrid low-dissipative/shock-capturing capabilities and the time advancement is performed using a Runge–Kutta scheme.

Suitability of an Artificial Viscosity Model for Compressible Under-Resolved Turbulence Using a Flux Reconstruction Method

In the simulation of compressible turbulent flows via a high-order flux reconstruction framework, the artificial viscosity model plays an important role to ensure robustness in the strongly compressible region. However, the impact of the artificial viscosity model in under-resolved regions on dissipation features or resolving ability remains unclear. In this work, the performance of a dilation-based (DB) artificial viscosity model to simulate under-resolved turbulent flows in a high-order flux reconstruction (FR) framework is investigated. Comparison is conducted with results via several typical explicit subgrid scale (SGS) models as well as implicit large eddy simulation (iLES) and their impact on important diagnostic quantities including turbulent kinetic energy, total dissipation rate of kinetic energy, and energy spectra are discussed. The dissipation rate of kinetic energy is decomposed into several components including those resulting from explicit SGS models or Laplacian artificial viscosity model; thus, an explicit evaluation of the dissipation rate led by those modeling terms is presented. The test cases consist of the Taylor-Green vortex (TGV) problem at Re=1600, the freely decaying homogeneous isotropic turbulence (HIT) at Mat0=0.5 (the initial turbulent Mach number ), the compressible TGV at Mach number 1.25 and the compressible channel flow at Reb= 15,334 (the bulk Reynolds number based on bulk density, bulk velocity and half-height of the channel), Mach number 1.5. The first two cases show that the DB model behaves similarly to the SGS models in terms of dissipation and has the potential to improve the insufficient dissipation of iLES with the fourth-order-accurate FR method. The last two cases further demonstrate the ability of the DB method on compresssible under-resolved turbulence and/or wall-bounded turbulence. The results of this work suggest the general suitability of the DB model to simulate under-resolved compressible turbulence in the high order flux reconstruction framework and also suggest some future work on controlling the potential excessive dissipation caused by the dilation term.

An implicit large eddy simulation method based on all-speed schemes

It remains a challenge for ILES methods to provide physical consistent viscosity in real applications which comprise complex flow structures in both high and low Mach numbers regimes. For these, we analyze an Implicit Large Eddy Simulation (ILES) method based upon all-speed schemes in a framework of the finite volume method in this study. This method can accurately capture both compressible phenomena such as shock waves as well as small turbulent structures. With a detailed analysis of the numerical viscosity and effective eddy viscosities in physical and spectral spaces, the method is verified to be suitable for the simulation of compressible turbulent flows. After it, the derived ILES method is applied to the simulation of a cylinder flow and a transonic cavity flow. Both results are in good agreements with the previous LES or experimental data. These results indicate that it is promising to study the application of the all-speed scheme to the ILES of complex engineering flow problems.

Entropy-stable schemes in the low-Mach-number regime: Flux-preconditioning, entropy breakdowns, and entropy transfers

Entropy-Stable (ES) schemes, specifically those built from Tadmor (1987) [54], have been gaining interest over the past decade, especially in the context of under-resolved simulations of compressible turbulent flows using high-order methods. These schemes are attractive because they can provide stability in a global and nonlinear sense (consistency with thermodynamics). However, fully realizing the potential of ES schemes requires a better grasp of their local behavior. Entropy-stability itself does not imply good local behavior (Gouasmi et al., 2019 [17], Gouasmi et al., 2020 [18]). In this spirit, we studied ES schemes in problems where global stability is not the core issue. In the present work, we consider the accuracy degradation issues typically encountered by upwind-type schemes in the low-Mach-number regime (Turkel, 1999 [59]) and their treatment using Flux-Preconditioning (Turkel, 1987 [58], Miczek et al., 2015 [41]). ES schemes suffer from the same issues and Flux-Preconditioning can improve their behavior without interfering with entropy-stability. This is first demonstrated analytically: using similarity and congruence transforms we were able to establish conditions for a preconditioned flux to be ES, and introduce the ES variants of the Miczek's and Turkel's preconditioned fluxes. This is then demonstrated numerically through first-order simulations of two simple test problems representative of the incompressible and acoustic limits, the Gresho Vortex and a right-moving acoustic wave. The results are overall consistent with previous studies. For instance, we observe that Turkel's preconditioner improves accuracy in the incompressible limit with the downside of overly damping acoustic waves (Bruel et al., 2019 [4]). For Miczek's matrix however, we came across unexpected spurious transients in both problems (a small left-moving acoustic wave in the latter), motivating further analysis. We revisited the pressure fluctuation argument of Guillard and Viozat (1999) [26] in terms of entropy, showing how the standard ES dissipation operator (Ismail and Roe, 2009 [30]) can introduce inconsistent discrete entropy fluctuations in space. These analytical results are achieved by introducing mode-by-mode decompositions of the dissipation operator, similar to Roe and Pike (1984) [51], Tadmor (2003) [55], leading to what we call discrete Entropy Production Breakdowns (EPBs) in space. These EPBs outline the contributions of convective and acoustic modes to the discrete entropy production, both locally and globally. Ultimately, these EPBs enable us to single-out in the ES Miczek flux a skew-symmetric matrix component which we believe causes entropy transfers between acoustic waves. Removing this contribution eliminates the spurious transients without interfering with entropy-stability. This conjecture is explored numerically and analytically.

Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness

In the approximation of one-fluid hydrodynamics, a closed system of Favre-averaged magneto-hydrodynamic equations is formulated, intended for the numerical simulation of compressible turbulent flows of electrically conductive media in the presence of a magnetic field. Special emphasis is paid to the method of obtaining, within the framework of irreversible thermodynamics, the constitutive relations for the turbulent flux heat and the total (kinetic plus magnetic) tensor of turbulent stresses. A new approach to modeling the coefficient of turbulent kinematic viscosity for an astrophysical disk is proposed, which takes into account the influence of an external and generated magnetic field, as well as the processes of convective heat transfer on turbulence in a stratified layer of finite thickness, and thereby modifies the Shakura–Sunyaev alpha formalism developed by for a thin disk and widely used in the astrophysical literature.

Heterogeneous CPU+GPU parallelization for high-accuracy scale-resolving simulations of compressible turbulent flows on hybrid supercomputers

A heterogeneous parallel algorithm for simulation of compressible turbulent flows and its portable software implementation are presented. The underlying numerical method is based on a family of higher accuracy edge-based reconstruction schemes on unstructured mixed-element meshes. The proposed parallel solution can engage a large number of computing devices of most of the existing computing architectures used in modern supercomputers, including manycore CPUs and GPUs. It is capable of co-execution on both CPUs and accelerators simultaneously. The multilevel parallel algorithm combines: MPI for distributing workload among hybrid cluster nodes and between devices inside nodes; OpenMP for manycore CPUs and other supporting devices, such as Intel Xeon Phi; OpenCL for massively-parallel accelerators, such as GPUs of various vendors, including NVIDIA, AMD, Intel. The main focus is on the adaptation of the numerical method and its computational algorithm to the stream processing parallel paradigm. The very limited device memory inherent in GPU computing is also taken into account. A detailed description of the parallel algorithm is presented, as well as the techniques used for its efficient parallel implementation. Special attention is paid to implicit time integration with its linear solver and calculation of convective fluxes and viscous terms. The use of mixed floating-point precision and overlapping communications and computations is also discussed. Parallel performance is demonstrated in practical applications on different kinds of supercomputers using up to 10 thousand cores and multiple GPUs of comparable overall performance.

Unsteady flow simulation of compressible turbulent flow in dual-bell nozzle with movement of extendible section from its initial to working position

The use of extendible nozzles in propulsion systems is one of the ways to increase the geometric degree of expansion of the nozzle and the thrust. Numerical simulation of a supersonic turbulent flow of a viscous compressible gas in an extendible nozzle is considered. The simulations performed take into account the movement of the extendible part of the nozzle from the its initial to the working position. The Reynolds-averaged Navier–Stokes equations and the equations of the SST turbulence model discretized on moving meshes are used for numerical calculations. The unsteady flowfield formed when the nozzle is brought to the working position is studied, and the topological features of the flow (separation, mixing, reattachment, secondary flow), and the spatial and temporal distributions of flow quantities are investigated. The distributions of pressure at different times and the axial force applied to the inner walls of the nozzle during the outflow of a supersonic underexpanded jet from the nozzle are discussed. The distributions of flow quantities computed with unsteady and quasi-state formulations of the problem are compared.

High-order gas-kinetic scheme with parallel computation for direct numerical simulation of turbulent flows

The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime [9]. Due to the multi-scale nature and coupled temporal-spatial evolution process, HGKS provides a valid tool for the numerical simulation of compressible turbulent flow. Based on the domain decomposition and message passing interface (MPI), a parallel HGKS code is developed for large-scale computation in this paper. The standard tests from the nearly incompressible flow to the supersonic one, including Taylor-Green vortex problem, turbulent channel flow and isotropic compressible turbulence, are presented to validate the parallel scalability, efficiency, accuracy and robustness of parallel implementation. The performance of HGKS for the nearly incompressible turbulence is comparable with the high-order finite difference scheme, including the resolution of flow structure and efficiency of computation. Based on the accuracy of the numerical solution, the numerical dissipation of the scheme in the turbulence simulation is quantitatively evaluated. Meanwhile, based on the kinetic formulation HGKS shows advantage for supersonic turbulent flow simulation with its accuracy and robustness. The current work demonstrates the capability of HGKS as a powerful DNS tool from the low speed to supersonic turbulence study, which is less reported under the framework of finite volume scheme.

STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows

We present STREAmS, an in-house high-fidelity solver for direct numerical simulations (DNS) of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interaction. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated with the solution of high-speed turbulent flows and can be used across a wide range of Mach numbers, extending from the low subsonic up to the hypersonic regime. From the computational viewpoint, STREAmS is oriented to modern HPC platforms thanks to MPI parallelization and the ability to run on multi-GPU architectures. This paper discusses the main implementation strategies, with particular reference to the CUDA paradigm, the management of a single code for traditional and multi-GPU architectures, and the optimization process to take advantage of the latest generation of NVIDIA GPUs. Performance measurements show that single-GPU optimization more than halves the computing time as compared to the baseline version. At the same time, the asynchronous patterns implemented in STREAmS for MPI communications guarantee very good parallel performance especially in the weak scaling spirit, with efficiency exceeding 97% on 1024 GPUs. For overall evaluation of STREAmS with respect to other compressible solvers, comparison with a recent GPU-enabled community solver is presented. It turns out that, although STREAmS is much more limited in terms of flow configurations that can be addressed, the advantage in terms of accuracy, computing time and memory occupation is substantial, which makes it an ideal candidate for large-scale simulations of high-Reynolds number, compressible wall-bounded turbulent flows. The solver is released open source under GPLv3 license. Program summaryProgram Title: STREAmSCPC Library link to program files:https://doi.org/10.17632/hdcgjpzr3y.1Developer’s repository link:https://github.com/matteobernardini/STREAmSCode Ocean capsule:https://codeocean.com/capsule/8931507/tree/v2Licensing provisions: GPLv3Programming language: Fortran 90, CUDA Fortran, MPINature of problem: Solving the three-dimensional compressible Navier–Stokes equations for low and high Mach regimes in a Cartesian domain configured for channel, boundary layer or shock-boundary layer interaction flows.Solution method: The convective terms are discretized using a hybrid energy-conservative shock-capturing scheme in locally conservative form. Shock-capturing capabilities rely on the use of Lax–Friedrichs flux vector splitting and weighted essentially non-oscillatory (WENO) reconstruction. The system is advanced in time using a three-stage, third-order RK scheme. Two-dimensional pencil distributed MPI parallelization is implemented alongside different patterns of GPU (CUDA Fortran) accelerated routines.

Acceleration of NOISEtte Code for Scale-Resolving Supercomputer Simulations of Turbulent Flows

The present work is devoted to accelerating the NOISEtte code and lowering its memory consumption. This code for scale-resolving supercomputer simulations of compressible turbulent flows is based on higher-accuracy methods for unstructured mixed-element meshes and hierarchical MPI $$+$$ OpenMP parallelization for cluster systems with manycore processors. We demonstrate modifications of the underlying numerical method and its parallel implementation, which consist, in particular, in using a simplified approximation method for viscous fluxes and mixed floating-point precision. The modified version has been tested on several representative cases. The performance measurements and validation results are presented.

Effect of Mach number on the compressible flow past a wavy-axis cylinder

Large-eddy simulations of compressible turbulent flow around wavy-axis cylinder have been carried out at Mach number M∞ varying from 0.55 to 0.95. A fixed Reynolds number is chosen, i.e., Re=2×105. Two different force behaviors as well as flow characteristics are obtained by wavy-axis cylinder, around the critical Mach number 0.9 relevant to transonic flow past a circular cylinder. For M∞<0.9, the effective drag reduction is obtained by wavy-axis cylinder with suppressing vortex shedding, which can be considered as the result of the reduced interaction between high- and low-momentum streams in the near wake. When M∞>0.9, the drag reduction vanishes, associated with the coexistence of unsteady and quasi-steady flow states and formation of strong oblique shock waves in the wake of wavy-axis cylinder. For all considered M∞, the turbulent fluctuations are very small in the near wake of wavy-axis cylinder, resulting in the lower fluctuating force on the body. The instability processes for wavy-axis cylinder are derived from the competition between the oblique waves and Kelvin-Helmholtz instability waves, associated with the large-scale vortex motion attenuating or vanishing as well as the low-intensity turbulence in the near wake. The analysis of dynamical mechanisms shows that wavy-axis cylinder only provide the effective drag reduction for compressible flow past circular cylinder involving large-scale vortex shedding. For the intermittent shock waves and permanent shock waves with large-scale movement, wavy-axis cylinder is an effective way for shock control. While, when the wake shock waves appear, say about M∞≥0.85, the wavy-axis cylinder is also invalid for shock control.

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

SummaryIn this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k − ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k − ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.

A kinetic energy preserving DG scheme applied to mechanical FSI

AbstractIn the context of mechanical fluid‐structure interaction (FSI) comprising moving or deforming structures, fluid discretizations need to cope with time‐dependent fluid domains and resulting grid deformations in addition to the general challenges regarding e.g. boundary layers and turbulent phenomena. Recent approaches in the simulation of compressible turbulent flow are based on so‐called split forms of conservation laws to guarantee the preservation of secondary physical quantities such as kinetic energy. For the simulation of turbulent flows, this often leads to a better representation of the kinetic energy spectrum. Initially, kinetic energy preserving(KEP) DG schemes have been constructed on Gauss‐Legendre‐Lobatto(GLL) nodes containing the interval end points, however, KEP DG schemes based on the classical Gauss‐Legendre(GL) nodes are potentially more accurate and may be also more efficient than its GLL variant for certain applications. In this work, the KEP‐DG schemes both on GL and GLL nodes are applied to the classical moving piston test case via an ALE formulation on moving fluid grids showing a more accurate frequency representation of the structure displacement in case of GLL nodes. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary Reynolds- Averaged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k − ω turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k − ω turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

Direct Numerical Simulation of Compressible Turbulent Flows Through a Square Duct at low and intermediate Reynolds Numbers

Direct Numerical Simulation of Compressible Turbulent Flows Through a Square Duct at low and intermediate Reynolds Numbers

GPU‐accelerated direct numerical simulations of decaying compressible turbulence employing a GKM‐based solver

SummaryGas Kinetic Method‐based flow solvers have become popular in recent years owing to their robustness in simulating high Mach number compressible flows. We evaluate the performance of the newly developed analytical gas kinetic method (AGKM) by Xuan et al. in performing direct numerical simulation of canonical compressible turbulent flow on graphical processing unit (GPU)s. We find that for a range of turbulent Mach numbers, AGKM results shows excellent agreement with high order accurate results obtained with traditional Navier–Stokes solvers in terms of key turbulence statistics. Further, AGKM is found to be more efficient as compared with the traditional gas kinetic method for GPU implementation. We present a brief overview of the optimizations performed on NVIDIA K20 GPU and show that GPU optimizations boost the speedup up‐to 40x as compared with single core CPU computations. Hence, AGKM can be used as an efficient method for performing fast and accurate direct numerical simulations of compressible turbulent flows on simple GPU‐based workstations. Copyright © 2016 John Wiley &amp; Sons, Ltd.