A new method to solve poisson equation with Neumann boundary conditions.

In this paper a new numerical method to solve a pressure Poisson equation with Neumann boundary conditions is presented. The Poisson equation with Neumann boundary conditions is divided into two equations. One is the Poisson equation with Dirichlet boundary conditions at the whole boundary, which can be solved by the conventional checkerboard SOR method with a reasonable convergence, and the other is the Laplace equation with boundary conditions obtained by taking the derivative of the solution so as to satisfy the Neumann boundary conditions for the original equation. The latter can be quickly solved by the BEM at least at the boundaries. The solutions at the interior points can be calculated by the BEM or solving the Laplace equation with Dirichlet boundary conditions by the checkerboard SOR method to reduce CPU time. Consequently, the solution of the original equation is obtained as the sum of each solution. This method is applied to the primitive variable procedure to solve the incompressible flow around a circular cylinder at the Reynolds number of 105, which produces a converged pressure solution at every time step and the time-averaged drag coefficient close to the experiment.