Numerical Solutions for the Pressure Poisson Equation with Neumann Boundary Conditions Using a Nonstaggered Grid, I
Abstract
Numerical solutions are obtained for the pressure Poisson equation with Neumann boundary conditions using a nonstaggered grid. The existence of a solution for this equation requires the satisfaction of a compatibility condition which relates the source of the Poisson equation and the Neumann boundary conditions. This compatibility condition is not automatically satisfied on nonstaggered grids. Failure to satisfy the compatibility condition leads to nonconvergent iterative solutions. Consistent finitedifference approximations for the pressure equation with Neumann boundary conditions are developed to satisfy the compatibility condition on nonstaggered grids. The method is applied to calculate the pressure coefficient in a driven cavity when given the velocity field. The velocity is computed from the stream functionvorticity formulation of the NavierStokes equations.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1987
 DOI:
 10.1016/00219991(87)900088
 Bibcode:
 1987JCoPh..70..182A
 Keywords:

 Boundary Conditions;
 Incompressible Flow;
 Iterative Solution;
 Neumann Problem;
 Poisson Equation;
 Pressure Distribution;
 Velocity Distribution;
 Computational Grids;
 Continuity Equation;
 NavierStokes Equation;
 Reynolds Number;
 Stream Functions (Fluids);
 Vorticity;
 Fluid Mechanics and Heat Transfer