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AN IMPROVED VARIABLE DENSITY PRESSURE PROJECTION SOLVER FOR ADAPTIVE MESHES

Abstract. Tatebe [17] introduced the multigrid preconditioned conjugate gradient method (MGPCG) for solving the sparse matrix system that results from discretizing an elliptic equation with discontinuous coefficients and source terms. Tatebe’s work was restricted to elliptic problems on a single structured grid. We present a MGPCG algorithm for an adaptive hierarchy of grids, and we show analytically that our method is guaranteed to converge. Using our new MGPCG algorithm to solve the projection equation, we report results for incompressible two-phase flow problems, and for incompressible flow in complex geometries. It is found that the new method is about twice as fast as the MG method proposed in [13, 14], about three times as fast as the PCG method proposed in [8] and that the new method scales well with increasing AMR levels.