A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number

Abstract

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.