MULTIGRID DOMAIN DECOMPOSITION APPROACH FOR SOLUTION OF NAVIER-STOKESEQUATIONS IN PRIMITIVE VARIABLE FORM

A new multi-grid (two-grid) pseudospectral element method has been car ried out for solution of incompressible flow in terms of primitive var iable formulation. The main objective of the proposed method is to app ly the multi-grid technique solving the incompressible flow problems a ssociated with three commonly encountered multi-grid environments. In domain decomposition terminology, it includes (I) partially overlapped subdomains, each of which has same types of grids; (II) partially ove rlapped subdomains, each of which has different types of grids; (III) local adaptive subdomains fully overlapped with the original computati onal domain (composite grids). The approach for flow problems, complex geometry or not, is to first divide the computational domain into a n umber of subdomains with the inter-overlapping area (partially or full y overlapped). In categories I and II, the fine-grid or coarse-grid su bdomains can be defined by their representation, while in category III the fine-grid or coarse-grid subdomains are defined as usual. Next, i mplement the Schwarz Alternating Procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove t he high frequency error that occurs when the data interpolation from t he fine-grid subdomain to the coarse-grid subdomain is conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of velocity field, which intrinsically links the press ure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansi on technique or preconditioned method with the least storage requireme nt, i.e. O(N2) in 2-D. Numerical results of (i) driven cavity flow (Re = 100, 400) with Cartesian grids (category I) in each subdomain, (ii) driven cavity flow (Re = 3200) with local adaptive grids (category II I) in each subdomain, and (iii) flow over a cylinder (Re = 250) with ' O' grids in one subdomain and Cartesian grids in another (category II) will be presented in the paper to account for the versatility of the proposed multi-grid method.