Simulation Of Incompressible Turbulent Flows Research Articles

Subgrid-scale model for large eddy simulations of incompressible turbulent flows within the lattice Boltzmann framework

Subgrid-scale model for large eddy simulations of incompressible turbulent flows within the lattice Boltzmann framework

Neural networks for large eddy simulations of wall-bounded turbulence: numerical experiments and challenges.

We examine the application of neural network-based methods to improve the accuracy of large eddy simulations of incompressible turbulent flows. The networks are trained to learn a mapping between flow features and the subgrid scales, and applied locally and instantaneously-in the same way as traditional physics-based subgrid closures. Models that use only the local resolved strain rate are poorly correlated with the actual subgrid forces obtained from filtering direct numerical simulation data. We see that highly accurate models in a priori testing are inaccurate in forward calculations, owing to the preponderance of numerical errors in implicitly filtered large eddy simulations. A network that accounts for the discretization errors is trained and found to be unstable in a posteriori testing. We identify a number of challenges that the approach faces, including a distribution shift that affects networks that fail to account for numerical errors.

High-Order WENO-based Semi-Implicit Projection Method for Incompressible Turbulent Flows: Development, Accuracy, and Reynolds Number Effects

A novel high-order projection method is presented in this study for the simulation of incompressible turbulent flows, utilising weighted essentially non-oscillatory (WENO) schemes. Spatial discretization involves using WENO schemes for nonlinear convection and standard central differences (CD) for the viscous term. The approach combines various orders of WENO and central difference schemes (WENO3/CD2, WENO5/CD4, and WENO7/CD6) to achieve third, fifth, and seventh-order spatial accuracy for velocity fields, respectively. Validating this method involved a thorough examination using the 2D Taylor Green vortex problem in both space and time, along with simulations of 3D Taylor-Green vortex problems at increasing Reynolds numbers (Re) of 1, 600, 16, 000, and 160, 000. The outcomes encompassed analyses of kinetic energy, enstrophy, energy spectra, and vortex fields, indicating the method's effectiveness in accurately simulating high Reynolds number turbulent flows without additional sub-grid scale models.

A Cartesian Immersed Boundary Method Based on 1D Flow Reconstructions for High-Fidelity Simulations of Incompressible Turbulent Flows Around Moving Objects

The aim of the present numerical study is to show that the recently developed Alternating Direction Reconstruction Immersed Boundary Method (ADR-IBM) (Giannenas and Laizet in Appl Math Model 99:606–627, 2021) can be used for Fluid–Structure Interaction (FSI) problems and can be combined with an Actuator Line Model (ALM) and a Computer-Aided Design (CAD) interface for high-fidelity simulations of fluid flow problems with rotors and geometrically complex immersed objects. The method relies on 1D cubic spline interpolations to reconstruct an artificial flow field inside the immersed object while imposing the appropriate boundary conditions on the boundaries of the object. The new capabilities of the method are demonstrated with the following flow configurations: a turbulent channel flow with the wall modelled as an immersed boundary, Vortex Induced Vibrations (VIVs) of one-degree-of-freedom (2D) and two-degree-of-freedom (3D) cylinders, a helicopter rotor and a multi-rotor unmanned aerial vehicle in hover and forward motion. These simulations are performed with the high-order fluid flow solver Incompact3d which is based on a 2D domain decomposition in order to exploit modern CPU-based supercomputers. It is shown that the ADR-IBM can be used for the study of FSI problems and for high-fidelity simulations of incompressible turbulent flows around moving complex objects with rotors.

Law of incipient separation for turbulent flows over airfoils as inferred by Reynolds-averaged Navier–Stokes

Lu, Aithal, and Ferrante [“Law of incipient separation over curved ramps as inferred by Reynolds-averaged Navier–Stokes,” AIAA J. 59, 196–214 (2021)] discovered a law that predicts the incipience of flow separation over curved ramps by knowing only a few geometrical parameters of the ramp and the Reynolds number of the flow. In that spirit, we have searched for a similar law for airfoils by performing simulations of incompressible turbulent flows over 32 NACA (National Advisory Committee for Aeronautics) airfoils using Reynolds-averaged Navier–Stokes (RANS) equations. First, we have carried out verification and validation of RANS against the experimental measurements by A. J. Wadcock (“Investigation of low-speed turbulent separated flow around airfoils,” NASA Contractor Report No. 177450, 1987), which show the accuracy of the RANS prediction at small angles of attack when flow separation begins to occur on the upper side of the airfoil. Then, we have investigated the effects of the angle of attack, airfoil thickness, and camber on the incipience of flow separation for the Reynolds number based on airfoil chord Rec∈[1.64×106,6×106]. From the analysis of the RANS results, we have determined a law for predicting the incipience of turbulent flow separation over airfoils that relies only on airfoil's newly defined characteristic slope, thickness, camber, and Rec.

Wall model‐based diffuse‐interface immersed boundary method for simulation of incompressible turbulent flows

AbstractIn this work, a method is proposed to simulate the high Reynolds number turbulent flows by combining the diffuse‐interface immersed boundary method (IBM) with different wall models. In this method, two auxiliary layers (a series of Lagrangian points) are set outside the wall: the reference layer and the enforced layer. The wall model is applied at the reference layer to calculate the wall shear stress and the boundary condition is implemented at the enforced layer. When implementing the boundary condition, the implicit velocity correction‐based IBM is used. This process requires the velocity at the enforced layer. To calculate the velocity at the enforced layer, the momentum equation is integrated along the normal direction of the wall to link the tangential component of the velocity to the wall shear stress predicted by the wall models, and the normal component of the velocity is approximately reconstructed by the parabolic distribution. In addition, the Reichardt's law combined with Spalding's formula is utilized to determine the integral length. Numerical experiments for the turbulent flows around the flat plate, the NACA0012 airfoil and the NACA23012 airfoil are carried out to verify the feasibility of this method.

A Cell-Based Smoothed Finite Element Method for Solving Incompressible Reynolds-Averaged Navier–Stokes Equations Using Spalart–Allmaras Turbulence Model

In this paper, a leap forward in the development of a cell-based smoothed finite element method (CS-FEM) is presented to solve incompressible turbulent flow treated by Reynolds–averaged Navier–Stokes (RANS) equations and the Spalart–Allmaras (SA) model. The streamline-upwind/Petrov–Galerkin stabilization combined with the stabilized pressure gradient projection (SUPG/SPGP) is used to address oscillation and instability for CS-FEM in calculations of incompressible flow. The capability, accuracy, and validity of presented turbulent CS-FEM were tested by four numerical examples, including turbulent channel flow, a backward-facing step, flow past a circular cylinder, and turbulent flow past multistage Tesla valves. Based on the favorable comparison of numerical results obtained by the presented CS-FEM with experimental results and literature numerical results, CS-FEM is demonstrated to be highly applicable with appealing performances on simulations of incompressible turbulent flows. This new extension of CS-FEM empowers the S-FEM family to solve complex turbulent flows.

Turbulent kinetic dissipation analysis for residual-based large eddy simulation of incompressible turbulent flow by variational multiscale method

The underlying physical mechanism of the residual-based large eddy simulation (LES) based on the variational multiscale (VMS) method is clarified. Resolved large-scale energy transportation equation is mathematically derived for turbulent kinetic energy budget analysis. Firstly, statistical results of benchmark turbulent channel flow at Reτ=180 obtained using a coarse mesh are compared with the results obtained by the classical LES with the Smagorinsky and dynamic subgrid stress (SGS) model. The present LES shows an advantage in predicting the statistical results of the incompressible turbulent flows. Secondly, the contributions of the unresolved small-scale presentation terms (Term I-IV in Eq. (10)) to the turbulent kinetic dissipation are analysed for the VMS method. The results show that the turbulent kinetic dissipation provided by the numerical diffusion in the VMS method is smaller in the inner layer, larger in the outer layer of the channel flow than those by the Smagorinsky and dynamic SGS model. The turbulent kinetic dissipation in the VMS method is mainly given by the numerical diffusion provided by one of the “cross-stress” terms (Term I, same as the stabilization term in the SUPG method) and LSIC term (Term IV). The other one of the “cross-stress” terms (Term II) gives rise to the positive turbulent kinetic energy budget, and does not dissipate the turbulent kinetic energy. The so-called “Reynolds stress” term (Term III) dissipates the turbulent energy but provides a very small numerical diffusion. Finally, on the basis of the turbulent kinetic energy dissipation analysis, a new residual-based stabilized finite element formulation is proposed by modifying the large-scale equation in the VMS method. Numerical experiments of 2D lid-driven cavity flow and 3D incompressible turbulent channel flow are tested to validate the proposed formulation. It is shown that all the stabilization terms in the proposed formulation produce additional numerical diffusions and physically increase the total turbulent kinetic dissipation. Consequently, an apparent improvement in both the first-order and second-order statistical quantities are pursued by the new stabilized finite element formulation.

Variationally derived closure models for large eddy simulation of incompressible turbulent flows

AbstractWe present a variationally consistent method for deriving residual‐based closure models for incompressible Navier–Stokes equations. The method is based on the fine‐scale variational structure facilitated by the variational multiscale framework where fine scales are driven by the residuals of the Euler–Lagrange equations of the resolved scales in the balance of momentum and conservation of mass equations. A bubble‐functions based approach is applied directly to the fine‐scale variational equation to derive analytical expressions for the closure model. Variational consistency of the model lends itself to rigorous linearization that results in quadratic rate of convergence of the method in the iterative solution strategy for the nonlinear equations. The method is shown to work for a family of linear and quadratic hexahedral and tetrahedral elements as well as composite discretizations that are comprised of hexahedral and tetrahedral elements in the same computational domain. Numerical tests with the proposed model are presented for various classes of turbulent flow problems to show its generality and range of applicability. The test cases investigated include Taylor–Green vortex stretching, statistically stationary wall‐bounded channel flows, and modeling the effects of the geometry of the leading edge of the plate on the instability of the boundary layer that leads to flow separation and flow reversal over flat plates of finite thickness.

A symmetry-preserving second-order time-accurate PISO-based method

A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method.Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods.

A high-throughput hybrid task and data parallel Poisson solver for large-scale simulations of incompressible turbulent flows on distributed GPUs

The solution of the pressure Poisson equation arising in the numerical solution of incompressible Navier–Stokes equations (INSE) is by far the most expensive part of the computational procedure, and often the major restricting factor for parallel implementations. Improvements in iterative linear solvers, e.g. deploying Krylov-based techniques and multigrid preconditioners, have been successfully applied for solving the INSE on CPU-based parallel computers. These numerical schemes, however, do not necessarily perform well on GPUs, mainly due to differences in the hardware architecture. Our previous work using many P100 GPUs of a flagship supercomputer showed that porting a highly optimized MPI-parallel CPU-based INSE solver to GPUs, accelerates significantly the underlying numerical algorithms, while the overall acceleration remains limited (Zolfaghari et al. [3]). The performance loss was mainly due to the Poisson solver, particularly the V-cycle geometric multigrid preconditioner. We also observed that the pure compute time for the GPU kernels remained nearly constant as grid size was increased. Motivated by these observations, we present herein an algebraically simpler, yet more advanced parallel implementation for the solution of the Poisson problem on large numbers of distributed GPUs. Data parallelism is achieved by using the classical Jacobi method with successive over-relaxation and an optimized iterative driver routine. Task parallelism is enhanced via minimizing GPU-GPU data exchanges as iterations proceed to reduce the communication overhead. The hybrid parallelism results in nearly 300 times less time-to-solution and thus computational cost (measured in node-hours) for the Poisson problem, compared to our best-case scenario CPU-based parallel implementation which uses a preconditioned BiCGstab method. The Poisson solver is then embedded in a flow solver with explicit third-order Runge-Kutta scheme for time-integration, which has been previously ported to GPUs. The flow solver is validated and computationally benchmarked for the transition and decay of the Taylor-Green Vortex at Re=1600 and the flow around a solid sphere at ReD=3700. Good strong scaling is demonstrated for both benchmarks. Further, nearly 70% lower electrical energy consumption than the CPU implementation is reported for Taylor-Green vortex case. We finally deploy the solver for DNS of systolic flow in a bileaflet mechanical heart valve, and present new insight into the complex laminar-turbulent transition process in this prosthesis.

Hierarchical Adaptive Eddy-Capturing Approach for Modeling and Simulation of Turbulent Flows

A short review of wavelet-based adaptive methods for modeling and simulation of incompressible turbulent flows is presented. Wavelet-based computational modeling approaches of different fidelities are recast into an integrated hierarchical adaptive eddy-capturing turbulence modeling framework. The wavelet threshold filtering procedure and the associated wavelet-filtered Navier–Stokes equations are briefly discussed, along with the adaptive wavelet collocation method that is used for numerical computations. Depending on the level of wavelet thresholding, the simulation is possibly supplemented with a localized closure model. The latest advancements in spatiotemporally varying wavelet thresholding procedures along with the adaptive-anisotropic wavelet-collocation method make the development of a fully adaptive approach feasible with potential applications for complex turbulent flows.

A hierarchical parallel implementation for heterogeneous computing. Application to algebra-based CFD simulations on hybrid supercomputers

The quest for new portable implementations of simulation algorithms is motivated by the increasing variety of computing architectures. Moreover, the hybridization of high-performance computing systems imposes additional constraints, since heterogeneous computations are needed to efficiently engage processors and massively-parallel accelerators. This, in turn, involves different parallel paradigms and computing frameworks and requires complex data exchanges between computing units. Typically, simulation codes rely on sophisticated data structures and computing subroutines, so-called kernels, which makes portability terribly cumbersome. Thus, a natural way to achieve portability is to dramatically reduce the complexity of both data structures and computing kernels. In our algebra-based approach, the scale-resolving simulation of incompressible turbulent flows on unstructured meshes relies on three fundamental kernels: the sparse matrix-vector product, the linear combination of vectors and the dot product. It is noteworthy that this approach is not limited to a particular kind of numerical method or a set of governing equations. In our code, an auto-balanced multilevel partitioning distributes workload among computing devices of various architectures. The overlap of computations and multistage communications efficiently hides the data exchanges overhead in large-scale supercomputer simulations. In addition to computing on accelerators, special attention is paid at efficiency on manycore processors in multiprocessor nodes with significant non-uniform memory access factor. Parallel efficiency and performance are studied in detail for different execution modes on various supercomputers using up to 9,600 processor cores and up to 256 graphics processor units. The heterogeneous implementation model described in this work is a general-purpose approach that is well suited for various subroutines in numerical simulation codes.

P-Multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the computational expense of solving large scale equation systems characterized by indefinite Jacobian matrices has often prevented the simulation of industrially-relevant computations. In this work we seek to improve the efficiency of Rosenbrock-type linearly-implicit Runge-Kutta methods by devising robust, scalable and memory-lean solution strategies. In particular, we introduce memory saving p-multigrid preconditioners coupling matrix-free and matrix-based Krylov iterative smoothers. The p-multigrid preconditioner relies on cheap element-wise block-diagonal smoothers on the fine space to reduce assembly costs and memory allocation, and ensures an adequate resolution of the coarsest space of the multigrid iteration using Additive Schwarz smoothers to obtain satisfactory convergence rates and optimal parallel efficiency of the method. In addition, the use of specifically crafted rescaled-inherited coarse operators to overcome the excess of stabilization provided by the standard inheritance of the fine space operators is explored. Extensive numerical validation is performed. The Rosenbrock formulation is applied to test cases of growing complexity: the laminar unsteady flow around a two-dimensional cylinder at Re=200 and around a sphere at Re=300, the transitional flow problem of the ERCOFTAC T3L test case suite with different levels of free-stream turbulence. As proof of concept, the numerical solution of the Boeing rudimentary landing gear test case at Re=106 is reported. A good agreement of the solutions with experimental data is documented, whereas a reduction in memory footprint of about 92% and an execution time gain of up to 3.5 is reported with respect to state-of-the-art solution strategies.

An assessment of two classes of variational multiscale methods for the simulation of incompressible turbulent flows

A numerical assessment of two classes of variational multiscale (VMS) methods for the simulation of incompressible flows is presented. Two types of residual-based VMS methods and two types of projection-based VMS methods are included in this assessment. The numerical simulations are performed at turbulent channel flow problems with various friction Reynolds numbers. It turns out the residual-based VMS methods, in particular when used with a pair of inf–sup stable finite elements, give usually the most accurate results for second order statistics. For this pair of finite element spaces, a flexible GMRES method with a Least Squares Commutator (LSC) preconditioner proved to be an efficient solver.

High-order accurate simulation of incompressible turbulent flows on many parallel GPUs of a hybrid-node supercomputer

Turbulent incompressible flows play an important role in a broad range of natural and industrial processes. High-order direct numerical simulations are often used for resolving the spatio-temporal scales of such flows. Such high-fidelity simulations require an extensive computational layout which often results in prohibitive computational costs. Recent advances in modern computing platforms, such as GPU-powered hybrid-node supercomputers, appear to become an enabler for high-fidelity CFD at large scales. In this work, we propose methods for accelerating a distributed-memory high-order incompressible Navier–Stokes solver by using NVIDIA Pascal GPUs of a Cray XC40/50 supercomputer. Arithmetically intensive or chronically invoked routines were ported to the GPUs using CUDA C. Host-side driver routines were developed to invoke CUDA C “external” kernels from the FORTRAN legacy code. Numerical methods, for some of the most intensive operations, namely multigrid preconditioners, were modified to be suited to the SIMD standard for graphics processors. Customized unit testing was performed to ensure double-precision accuracy of GPU computations. The optimization layer maintained the memory structure of the legacy code. Post-profiling confirms that backbone distributed memory communications increase the number of dynamic CPU–GPU memory copies, which offsets a part of the computational performance. Strong scalability of the entire flow solver and of the stand-alone pressure solver has been examined on up to 512 P100 GPUs. Strong scaling efficiency decreased for higher numbers of GPUs, probably due to a less favorable communication-to-computation ratio. Weak scalability of the entire solver was tested on up to 4096 P100 GPUs for two problems of different sizes. The solver maintained nearly ideal weak scalability for the larger problem, illustrating the potential of GPUs in dealing with highly resolved flows. The GPU-enabled solver is finally deployed for the scale-resolving simulation of flow transition in the wake of a solid sphere at Re=3700, by utilizing 192 GPUs. The time-averaged pressure coefficient along the sphere surface was in good agreement with previously reported data acquired from CPU-based direct numerical simulations and experiments.

Numerical simulation of incompressible turbulent flow in shrouded disk system with radial outflow

The flow behavior inside the shrouded disk system is of importance in appropriate design of turbomachinery cavities and turbine test cell hydraulics dynamometer. The turbulent incompressible flow is analyzed for the shrouded disk system with axial clearance. The flow core behaves as a Batchelor type structure when a weak inflow is imposed on the disk cavity. By increasing the inflow, the central core disappears and the tangential velocity distribution is changed to Stewartson type structure. The central core again reappears by increasing the Reynolds number. The moment coefficient of rotary disk depends on superimposed flow rate coefficient and dimensionless geometrical parameters. Moment coefficient increases with increasing inflow rate while the other parameters remain constant. The coefficient is reduced by increasing the Reynolds number. Moreover, it increases with both increasing rotary and stationary disks axial distance, and decreasing clearance ratio. The experimental results of a cavity with radial clearance are used to validate the accuracy of the simulation. The results of this analysis and its development can be used in the design of turbine test cell hydraulics dynamometers.

A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes

SummaryWe present a parallel fully implicit algorithm for the large eddy simulation (LES) of incompressible turbulent flows on unstructured meshes in three dimensions. The LES governing equations are discretized by a stabilized Galerkin finite element method in space and an implicit second‐order backward differentiation scheme in time. To efficiently solve the resulting large nonlinear systems, we present a highly parallel Newton‐Krylov‐Schwarz algorithm based on domain decomposition techniques. Analytic Jacobian is applied in order to obtain the best achievable performance. Two benchmark problems of lid‐driven cavity and flow passing a square cylinder are employed to validate the proposed algorithm. We then apply the algorithm to the LES of turbulent flows passing a full‐size high‐speed train with realistic geometry and operating conditions. The numerical results show that the algorithm is both accurate and efficient and exhibits a good scalability and parallel efficiency with tens of millions of degrees of freedom on a computer with up to 4096 processors. To understand the numerical behavior of the proposed fully implicit scheme, we study several important issues, including the choices of linear solvers, the overlapping size of the subdomains, and, especially, the accuracy of the Jacobian matrix. The results show that an exact Jacobian is necessary for the efficiency and the robustness of the proposed LES solver.

A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows

We present an efficient solver for massively-parallel direct numerical simulations of incompressible turbulent flows. The method uses a second-order, finite-volume pressure-correction scheme, where the pressure Poisson equation is solved with the method of eigenfunction expansions. This approach allows for very efficient FFT-based solvers in problems with different combinations of homogeneous pressure boundary conditions. Our algorithm explores all combinations of pressure boundary conditions valid for such a solver, in a single, general framework. The method is implemented in a 2D pencil-like domain decomposition, which enables efficient massively-parallel simulations. The implementation was validated against different canonical flows, and its computational performance was examined. Excellent strong scaling performance up to 104 cores is demonstrated for a domain with 109 spatial degrees of freedom, corresponding to a very small wall-clock time/time step. The resulting tool, CaNS, has been made freely available and open-source.

Preconditioned WENO finite-difference lattice Boltzmann method for simulation of incompressible turbulent flows

In this work, a preconditioned high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (WENO-LBM) is applied to deal with the incompressible turbulent flows. Two different turbulence models namely, the Spalart–Allmaras (SA) and k−ωSST models are used and applied in the solution method for this aim. The spatial derivatives of the two-dimensional (2D) preconditioned LB equation in the generalized curvilinear coordinates are discretized by using the fifth-order WENO finite-difference scheme and an implicit–explicit Runge–Kutta scheme is adopted for the time discretization. For the convective and diffusive terms of the turbulence transport equations, the third-order WENO and second-order central finite-difference schemes are used, respectively. The preconditioning technique along with the local time-stepping method are applied to the WENO-LBM to further accelerate the solution to the converged steady-state condition, and therefore, an accurate and efficient incompressible LB solver is provided for simulating turbulent flows. The accuracy and robustness of the proposed solution method are assessed by computing two test cases: the 2D turbulent flow over a flat plate at Re=1.0×107 and the 2D turbulent flow over a NACA0012 airfoil at Re=6.0×106 and different angles of attack. The present results are compared with the available numerical and experimental results which show excellent agreement. It is demonstrated that the present solution methodology based on the WENO-LBM provides more accurate results of the incompressible turbulent flows and it requires lower number of grid points compared to the traditional (low-order accurate) LB and Navier–Stokes solvers.