Simulation of complex incompressible flows using a finite element solver on MIMD machines

A 3-D incompressible unsteady flow solver based on simple finite elements with adaptive remeshing and grid movement for both moving and deforming surfaces is described. We demonstrate the combination of adaptive remeshing techniques with the incompressible flow solver with the computation of flow past an eel in 2-D and a blue-fin tuna in 3-D. The flow past a swimming tuna was computed for two extreme cases of the caudal fin frequency and swimming speed. A grid refinement study was performed and a grid converged solution for the force produced by the caudal fin was obtained.

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20° is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effectively used for the DNSs of the incompressible flows.

An improved HLLC-type solver for incompressible two-phase fluid flows

Present incompressible Navier-Stokes flow solver is developed in the framework of Building-Cube Method (BCM) which is based on a block-structured, high-density Cartesian mesh method. In this study, flow simulation around a formula-1 car which consists of 200 million cells was conducted by vector-parallel supercomputer NEC SX-9. For exploiting the performance of SX-9, the present flow solver was highly optimized for vector and parallel computation. In this paper, the computational result from the large scale simulation and the parallel efficiency in using flat-MPI or hybrid-MPI are discussed.

High fidelity computations were carried out to analyze the orbiter LH2 feedline flowliner. Computations were performed on the Columbia platform which is a 10,240-processor supercluster consisting of 20 Altix nodes with 512 processors each. Various computational models were used to characterize the unsteady flow features in the turbopump, including the orbiter Low-Pressure-Fuel-Turbopump (LPFTP) inducer, the orbiter manifold and an experimental test article used to represent the manifold. Unsteady flow originating from the orbiter LPFTP inducer is one of the major contributors to the high frequency cyclic loading that results in high cycle fatigue damage to the gimbal flowliners just upstream of the LPFTP. The flow fields for the orbiter manifold and representative test article are computed and analyzed for similarities and differences. An incompressible Navier-Stokes flow solver INS3D, based on the artificial compressibility method, was used to compute the flow of liquid hydrogen in each test article.

SummaryThis article concerns validation and verification (V&V) of the open source OpenFOAM incompressible flow solver that is widely used in both research and industry for the simulation of turbulent flows. Its numerical discretization scheme relies on classical finite volumes that are second order in space on regular grids. The solver is benchmarked using a challenging test case for which direct numerical simulation (DNS) reference data exist. The geometrical configuration of this flow is very simple, yet the behavior of the flow is 3D, complex, and unsteady, requiring an accurate flow solver to capture the associated physics. The physical problem addressed here requires huge computational grids. Computations are thus carried using parallel domain decomposition methods on a fairly large number of cores. The validation study performed here is particularly severe as it consists in comparing OpenFOAM results with DNS data obtained using high‐order codes. As simulations of turbulent flows require great computational resources, results concerning strong and weak scalability of the OpenFOAM flow solver are also presented. The performances of the code are assessed on two different HPC infrastructures. The experiences carried here show that OpenFOAM scales fairly up to 1000 cores on a Tier‐1cluster. The influences of the processor hardware and network topology are also highlighted. This study also provides profiling diagnostics thanks to the Integrated Performance Monitor (IPM).

The numerical simulation of incompressible viscous flows using primitive variable formulation requires that the pressure be obtained by solving the pressure Poisson equation (PPE). It is mentioned in the literature on incompressible flows [1,2] that when all the pressure boundary conditions are of Neumann type, then the pressure compatibility condition (PCC) has to be satisfied for guaranteeing the existence of solution. The main aim of this paper is to show that the PCC is not an important issue as has been claimed in the literature [1–3]. On the other hand, it will be shown that the crucial issue, in numerical simulation of incompressible viscous flows, is to ensure solenoidality of the velocity field accurately. We will further show that the accuracy of solenoidality depends on the choice of pressure boundary conditions. The demonstration is based on the computation for 2-D lid-driven cavity problem for Re=100 on 1292 uniform grid.

This paper presents a hybrid compressible–incompressible approach for simulating the Richtmyer–Meshkov instability (RMI) and associated mixing. The proposed numerical approach aims to circumvent the numerical deficiencies of compressible methods at low Mach (LM) numbers, when the flow has become essentially incompressible. A compressible flow solver is used at the initial stage of the interaction of the shock wave with the fluids interface and the development of the RMI. When the flow becomes sufficiently incompressible, based on a Mach number prescribed threshold, the simulation is carried out using an incompressible flow solver. Both the compressible and incompressible solvers use Godunov-type methods and high-resolution numerical reconstruction schemes for computing the fluxes at the cell interfaces. The accuracy of the model is assessed by using results for a two-dimensional (2D) single-mode RMI.

The complex fluid-structure interaction problem associated with the flow of blood through a heart valve with flexible leaflets is investigated both experimentally and numerically. In the experimental test rig, a pulse duplicator generates a pulsatile flow through a biomimetic rigid aortic root where a model of aortic valve with polymer flexible leaflets is implanted. High-speed recordings of the leaflets motion and particle image velocimetry measurements were performed together to investigate the valve kinematics and the dynamics of the flow. Large eddy simulations of the same configuration, based on a variant of the immersed boundary method, are also presented. A massively parallel unstructured finite-volume flow solver is coupled with a finite-element solid mechanics solver to predict the fluid-structure interaction between the unsteady flow and the valve. Detailed analysis of the dynamics of opening and closure of the valve are conducted, showing a good quantitative agreement between the experiment and the simulation regarding the global behavior, in spite of some differences regarding the individual dynamics of the valve leaflets. A multicycle analysis (over more than 20 cycles) enables to characterize the generation of turbulence downstream of the valve, showing similar flow features between the experiment and the simulation. The flow transitions to turbulence after peak systole, when the flow starts to decelerate. Fluctuations are observed in the wake of the valve, with maximum amplitude observed at the commissure side of the aorta. Overall, a very promising experiment-vs-simulation comparison is shown, demonstrating the potential of the numerical method.

Computations of three-dimensional incompressible flows by lattice Boltzmann method were executed on GPU successfully. The explicit and linear characteristic of lattice Boltzmann equation makes it very suitable to be solved on GPU and there is no any troublesome handling in making numerical code. As examples, 3D lid-driven cavity flow and the flow past a sphere were simulated by LBM and executed on GPU. As a result, for both cases, about 80-time accelerations over CPU computation were obtained. The performance of LBM solver for 3D single-phased incompressible flow is about 40 GFLOPS and the data transfer rate is about 70 GB/s.

Parallel Implicit Computation of Turbulent Transonic Flow around a Complete Aircraft Configuration

This paper presents stabilized finite element simulations of unsteady natural and mixed heat convection phenomena occurring in square enclosures. It is assumed that the enclosures are subject to intense uniform magnetic fields applied perpendicular to the vertical walls. It is well known that the classical Galerkin finite element method (GFEM) is prone to yielding nonphysical oscillations when simulating convection-dominated flows. Therefore, in order to handle such flows occurring at high Hartmann (0≤Ha≤100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 \\le {\\rm Ha} \\le 100$$\\end{document}) and Rayleigh (103≤Ra≤108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{3} \\le {\\rm Ra} \\le 10^{8}$$\\end{document}) numbers, the stabilization of the GFEM is accomplished with the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin formulations. Temporal discretizations are performed with the backward Euler formula. At each time step, the nonlinear systems are linearized with the Newton–Raphson (N–R) method, and the linearized systems are solved directly using the sparse lower–upper decomposition. The incompressible flow solvers are developed in-house, run in parallel within the FEniCS ecosystem, and tested on a comprehensive set of numerical experiments with various thermal boundary conditions. Numerical simulations and comparisons reveal that the proposed formulation performs quite well at high Hartmann and Rayleigh numbers without exhibiting any significant localized or globally spread numerical instabilities. Moreover, it achieves this by using uniform meshes and only linear elements, making the formulation much more computationally efficient. Mesh convergence analyses are also performed to demonstrate the reliability of the numerical results obtained.

Numerical simulation of incompressible flows using adaptive unstructured meshes and the pseudo-compressibility hypothesis

Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method

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