An Unstructured Parallel Least-Squares Spectral Element Solver for Incompressible Flow Problems

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.

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

A multidimensional characteristic-based method for making incompressible flow calculations on unstructured grids

A new method of treating incompressible flows with nonslip boundaries is proposed as an extension of the Fourier spectral method. This is characteristic in using the function subspace that is a hyperplane in the Fourier-transformed velocity space, prescribed by the boundary condition, as well as in taking the solenoidal field representation in the Fourier space so that the pressure term need not be involved in the main dynamics and then time-integration can simply be made by the high-order Runge-Kutta scheme. The method can be applied in a more complicated case with an active scalar. As examples, the flow transitions to turbulence in a channel and in a rectangular duct heated from below are treated.

Parallel FEM based on level set method for free-surface flow using PC cluster

Numerical simulation of incompressible flows through granular porous media

Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction

We investigate a domain decomposition method (DDM) of finite element method (FEM) using Intel's many integrated core (MIC) architecture in order to determine the most effective MIC usage. For this, recently introduced high-scalable parallel method of DDM is first introduced with a detailed procedure. Then, the Intel's Xeon Phi MIC architecture is presented to understand how to apply the parallel algorithm into a multicore architecture. The parallel simulation using the Xeon Phi MIC has an advantage that traditional parallel libraries such as the message passing interface (MPI) and the open multiprocessing (OpenMP) can be used without any additional libraries. We demonstrate the DDM using popular libraries for solving linear algebra such as the linear algebra package (LAPACK) or the basic linear algebra subprograms (BLAS). Moreover, both MPI and OpenMP are used for parallel resolutions of the DDM. Finally, numerical parallel efficiencies are validated by a two-dimensional numerical example.

Lattice Boltzmann method (LBM) is a new attractive computational approach for simulating isothermal multi-phase flows in computational fluid dynamics (CFD). It is based on the kinetic theory and easy to be parallelized. This study aims to analyze the performance of parallel LBM programming for the incompressible two-phase flows at high density and viscosity ratio. For this purpose, a liquid drop impact on a wetted wall with a pre-existing thin film of the same liquid is simulated by using the parallel LBM code. During the simulations, the domain decomposition, data communication and parallelization of the LBM code using the message passing interface (MPI) library have been investigated. The computational results show that the parallel LBM code exhibits a good high performance computing (HPC) on the parallel speed-up.

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

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.

A new class of normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse matrix techniques for solving efficiently sparse linear systems on distributed memory systems, using Message Passing Interface (MPI) communication library, is also presented along with theoretical estimates on speedups and efficiency. The implementation and performance on a distributed memory MIMD machine, using Message Passing Interface (MPI) is also investigated. Applications on characteristic initial/boundary value problems in three dimensions are discussed and numerical results are given.

In this work, we investigate devising efficient preconditioners for communication systems based on domain decomposition techniques. In particular, we focus on the uplink of a massive MIMO system and exploit the special structure of the channel cross-correlation matrix to derive improved preconditioners based on Schwarz preconditioning. Up to our knowledge, this is the first attempt to make use of domain decomposition techniques in the design of efficient preconditioners for communication systems. Two additive Schwarz preconditioners are investigated and tested within the context of cancelling inter-antenna interference in massive MIMO systems using two recently proposed parallel interference cancellation detectors. Simulation results reveal substantial improvement in convergence speed compared to the conventional Jacobi and block Jacobi preconditioning.

In this paper, we present a multi-parallel restricted additive Schwarz (MP-RAS) preconditioner construction method for cardiac electrophysiology simulation. This method is designed to address the need for solving large-scale linear systems in realistic cardiac electrophysiology simulations and can provide a more efficient computational tool for patient-specific electrical propagation modeling, arrhythmia studies, and the evaluation of ablation strategies. The proposed preconditioner is suitable for the finite element simulation of the anisotropic cardiac monodomain model. In particular, we construct the subdomains based on Morton code sorting, build submatrices by indices and decompose the formula for parallel computing. Given that the computing of each subdomain is relatively independent, the iteration can be extended to N-parallel. Numerical experiments indicate that for matrices of the same size and under the same number of partitions, Morton code sorting is at least 105 times faster than METIS, while the memory usages are reduced by 12∼32%. The iteration number is reduced by approximately two times compared with the Jacobi and block Jacobi preconditioned conjugate gradient (PCG) method. Comparative experiments with other solvers further demonstrate that the MP-RAS solver is highly efficient for solving this parabolic partial differential equation and have strong parallel scalability.

Parallel processing of Prestack Kirchhoff Time Migration on a PC Cluster