A Domain Decomposition Approach for Incompressible Flows Past Multiple Objects

Abstract

A domain decomposition approach has been developed to solve for flow around multiple objects. The method combines features of mask and multigrid algorithm implemented within the general framework of a primitive variable, pseudospectral elements formulation of fluid flow problems. The computational domain consists of a global rectangular domain, which covers the entire flow domain, and local subdomains associated with each object, which are fully overlapped with the rectangular domain. There are two key steps involved in calculating flow past multiple objects. The first step approximately solves the flow field by the mask method on the Cartesian grid alone, including on those grid points falling inside an object (a fuzzy boundary between the fluid-object interface), but with the restriction that the velocity on grid points within and on the surface of an object should be small or zero. The second step corrects the approximate flow field predicted from the first step by taking account of the object surface, i.e., solving the flow field on the local body-fitted (curvilinear) grid surrounding each object. A smooth data communication between the global and local grids can be implemented by the multigrid method when the Schwarz Alternating Procedure (SAP) is used for the iterative solution between the two overlapping grids. Numerical results for two-dimensional test problems for flow past elliptic cylinders are presented in the paper. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force (a negative drag coefficient) acting on the second one may occur during the vortex formation in the wake area of the first one.