Multi-grid domain decomposition approach for solution of Navier-Stokes equations in primitive variable form

Hwar-Ching Ku

Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Road, Laurel, MD 20723

Bala Ramaswamy

Department of Mechanical Engineering & Material Science, Rice University, Houston, Texas 77251


Abstract

The new multi-grid (or adaptive) pseudospectral element method has been carried out for solution of incompressible flow in terms of primitive variable formulation. The desired features of proposed method include (1) the ability to treat complex geometry; (2) the high resolution adapted in the interesting areas; (3) the minimal working space; and (4) effective under the multiple processors working environment.

The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of fine-grid and coarse-grid subdomains with the inter-overlapping area. Next, implement the Schwarz alternating procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine-grid subdomain to the coarse-grid subdomain are conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of velocity field, which intrinsicly links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique with the least storage requirement, i.e., O(N^{3}) in 3-D and O(N^{2}) in 2-D.

Numerical results of both driven cavity and jet flow will be presented in the paper to account for the versatility of proposed method.