FAST ITERATIVE SOLUTION OF POISSON EQUATION WITH NEUMANN BOUNDARY CONDITIONS IN NONORTHOGONAL CURVILINEAR COORDINATE SYSTEMS BY A MULTIPLE GRID METHOD

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Abstract
A simple multiple grid (MG) technique has been used to solve the linear system of equations arising from the finite-difference discretization of the Neumann problem for elliptic Poisson equations formulated in nonorthogonal curvilinear coordinate systems. Fast, flexible, and simple solution methods for such problems are mandatory when they should act as, for example, pressure solvers in hydrodynamic codes for incompressible fluid flow. The robustness of the solution method chosen can be derived from the fact that only strong nonorthogonal grids have some influence on the asymptotic convergence rate. Problems including patched coordinate systems-for example, with interfaces describing material discontinuities-can also be handled without loss of efficiency.