A Rapid and Accurate Solution for the Poisson Equation with Neumann Boundary Conditions on General Domains

摘要

This memorandum presents a rapid and accurate solution for the Poisson equation with Neumann boundary conditions on general domains. The stream-like function formulation is used to obtain two modified Poisson equations with Dirichlet boundary conditions. The first equation is solved for the flux components of the dependent variable, and are used in calculating Dirichlet boundary conditions for the second Poisson equation. Two integral constraints are to be satisfied in the present formulation. The first constraint is a consequence of Green's first integral theorem and the second constraint is a result of the present analysis. A new procedure is implemented in the boundary conditions to satisfy the second integral constraint. This technique is applied to calculate the static pressure from a Poisson equation with Neumann boundary conditions in the solution of Navier-Stokes equations (velocity pressure formulation). Numerical results for the incompressible viscous flow in a driven cavity are presented and compared with the available numerical results in the literature. (Author)