Two-point boundary-value problems applying Multi-grid method. Application to Poisson equation and partially parabolized Navier-Stokes equations.

Abstract

An efficiency of a Multi-grid method solving two-point boundary value problem is tested. First, Poisson equation is solved by a point - and a line - SOR methods with and without the Multi-grid procedure. Work Unit, indicating iteration number, and CPU time are compared. The effect of the application of the Multi-grid procedure is remarkable; e.g. for the case of point SOR method with 192x192 grid points, the equation can be solved about thirty times faster than the usual single grid method. Second, the present method is applied to a Partially Parabolized Navier-Stokes (PPNS) equations solver. It is confirmed that the method effectively works without any difficulty caused by a non-linear effect of the equations. Finally, an effective Multi-grid PPNS solver is proposed.