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A parallel solver for incompressible fluid flows

机译：用于不可压缩的流体流的平行求解器

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The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlin- earity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stokes equations into three Helmholtz equations and one Poisson equation. For each Helmholtz system, we apply the Alternating Direction Implicit (ADI) method resulting in three tridiagonal systems. The Poisson equation is solved using partial diagonalization which transforms the Laplacian operator into a tridiagonal one. We describe an implementation based on MPI where the computations are performed on each subdomain and information is exchanged on the interfaces, and where the tridiagonal system solutions are accelerated using vectorization techniques. We present performance results on a current multicore system.
机译：Navier-Stokes方程描述了一大类流体流动，但由于其非线性而难以分析解决。我们在本文中展示了一个平行的求解器，用于3-D Navier-Stokes方程，其不可抑制的不稳定流量流动，具有恒定系数，通过有限差分方法离散化。我们应用将Navier-Stokes方程转换为三个Helmholtz方程和一个泊松方程的预测投影方法。对于每个Helmholtz系统，我们应用交替方向隐式（ADI）方法，从而产生三个三角形系统。使用部分对角化解决泊松方程，其将拉普拉斯操作员转变为一个三角形。我们描述了基于MPI的实现，其中计算在每个子域内执行，并且在接口上交换信息，并且使用矢量化技术加速了三角形系统解决方案的位置。我们在当前的多核系统上呈现绩效结果。

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