USING DOMAIN DECOMPOSITION WITH CO-LOCATED FINITE VOLUME METHODS: TWO PROBLEMS AND TWO SOLUTIONS

摘要

In this paper, we discuss two problems which arise whenrndomain decomposition is used in conjunction with co-locatedrnfnite volume methods for solving the incompressible Navier-rnStokes equations.rnThe frst problem occurs when one tries to compute arnsolution to the pressure Poisson equation (PPE) over multiplerngrids. Two sources of interpolation error must be addressedrnbefore the PPE can be solved. One source results from therninterpolation of values from one grid to the boundary of arnneighboring grid, while the other, which is unique to co-locatedrnmethods, results from the interpolation of velocities from cellrncenters to cell faces. We have found that in order to obtainrna converged pressure equation, both the interpolation schemesrnmust be very accurate. Although our code is formally onlyrnsecond order in space, we use interpolation schemes whichrnare fourth order accurate for both intergrid and center-to-facerninterpolations.rnThe second problem occurs when using domain decomposi-rntion to solve problems in which the geometry includes re-entrantrncorners. We show that the natural way to apply domain decom-rnposition to a corner geometry results in unstable solutions. Tornremedy this problem, we employ L-shaped grids in our simula-rntions.