A Fast Poisson Solver for the Finite Difference Solution of the Incompressible Navier--Stokes Equations

Abstract

In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier--Stokes equations. To achieve our goal, new algorithms for diagonalizing a semidefinite pair are developed. The fast solver can also be extended to the three-dimensional case. The motivation and related issues in using this half-staggered grid are also discussed.