Moving Grid-Multigrid Fictitious Boundary Method for the Simulation of Viscous Flows Past Many Moving Disks

摘要

In this paper, multigrid fictitious boundary method (MFBM) coupled with moving grid method is presented to simulate numerically the viscous flows past many moving disks. The use of the multigrid FBM does not require to change the mesh during the simulations when the solid disks vary their positions. The advantage is that no expensive remeshing has to be performed. However, the accuracy for capturing the surfaces of solid disks is only of first order which might lead to accuracy problems. For a better approximation of the solid disk surfaces, r-type moving grid method is applied such that the accuracy for dealing with the interaction between the fluid and the disks can be highly improved. Only the solution of additional linear Poisson problems in every time step is required for generating the moving grid, which means that the additional work is significantly less than the main fluid-solid part. Several numerical examples of two elliptic and rectangular disks falling down in a channel with infinite length as well as sedimentation of 60 circular disks in a cavity filled with incompressible viscous flow are computed to show that the presented method is potentially powerful to simulate the viscous flows past many moving disks.