A solution to the pressure velocity coupling problem in computational fluid dynamics

Abstract

A new method is shown to provide a solution to the long standing pressure-velocity coupling problem encountered in pressure-based Computational Fluid Dynamics. This problem occurs when the dependent variables are colocated on the computational mesh. A solution was found by requiring that the interpolation equations, used to relate the velocity and density at the control volume faces to the nodal values, be constrained to conserve mass. This is referred to as Mass Constrained Interpolation. It also leads to a strategy for deriving and testing boundary conditions. The method is demonstrated by comparing one-dimensional computational solutions to exact solutions for a wide range of incompressible and compressible flows.

Keywords:

• Computational fluids
• pressure based
• p-V coupling
• incompressible
• compressible

Acknowledgments

Discussions with Paul Galpin were interesting and helpful. Gordon Stubley helped me understand the shock tube results. Thanks to De-Wei Yin for assisting with the manuscript preparation. Thanks also to my wife Cathy who tolerated many diversions of my attention while pondering p-V coupling.