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首页> 外文期刊>Journal of Scientific Computing >A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number
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A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number

机译：高雷诺数的3D非定常不可压缩流的并行域分解方法

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摘要

Numerical simulation of three-dimensional incompressible flows at high Reynolds number using the unsteady Navier-Stokes equations is challenging. In order to obtain accurate simulations, very fine meshes are necessary, and such simulations are increasingly important for modern engineering practices, such as understanding the flow behavior around high speed trains, which is the target application of this research. To avoid the time step size constraint imposed by the CFL number and the fine spacial mesh size, we investigate some fully implicit methods, and focus on how to solve the large nonlinear system of equations at each time step on large scale parallel computers. In most of the existing implicit Navier-Stokes solvers, segregated velocity and pressure treatment is employed. In this paper, we focus on the Newton-Krylov-Schwarz method for solving the monolithic nonlinear system arising from the fully coupled finite element discretization of the Navier-Stokes equations on unstructured meshes. In the subdomain, LU or point-block ILU is used as the local solver. We test the algorithm for some three-dimensional complex unsteady flows, including flows passing a high speed train, on a supercomputer with thousands of processors. Numerical experiments show that the algorithm has superlinear scalability with over three thousand processors for problems with tens of millions of unknowns.
机译：使用不稳定的Navier-Stokes方程对高雷诺数的三维不可压缩流进行数值模拟是具有挑战性的。为了获得精确的模拟，非常细的网格是必要的，并且这种模拟对于现代工程实践来说越来越重要，例如了解高速火车周围的流动行为，这是本研究的目标应用。为了避免CFL数和精细的空间网格大小所施加的时间步长约束，我们研究了一些完全隐式的方法，并着重研究如何在大型并行计算机上的每个时间步长求解大型非线性方程组。在大多数现有的隐式Navier-Stokes求解器中，采用了分离的速度和压力处理。在本文中，我们将重点放在牛顿-克里洛夫-舒瓦兹方法上，以解决由非结构网格上的Navier-Stokes方程完全耦合的有限元离散化引起的整体非线性系统。在子域中，LU或点块ILU用作局部求解器。我们在具有数千个处理器的超级计算机上针对某些三维复杂非稳态流（包括通过高速列车的流）测试该算法。数值实验表明，该算法具有超过3000个处理器的超线性可扩展性，可以解决数千万未知数的问题。

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