Abstract
The non-staggered(collocated) grid approach in which all the solution variables are located at the centers of control volumes is very popular for incompressible flow analyses because of its numerical efficiency on the curvilinear or unstructured grids. Rhie and Chow's paper is the first in using non-staggered grid method for SIMPLE algorithm, where pressure weighted interpolation was used to prevent decoupling of pressure and velocity. But it has been known that this non-staggered grid method has stability problems when pressure fields are nonlinear like in natural convection flows. Also Rhie-Chow scheme generates large numerical diffusion near curved walls. The cause of these unwanted problems is too large pressure damping term compared to the magnitude of face velocity. In this study the magnitude of pressure damping term of Rhie-Chow's method is limited to 1∼10% of face velocity to prevent physically unreasonable solutions. The wall pressure extrapolation which is necessary for cell-centered FVM is another source of numerical errors. Some methods are applied in a unstructured FV solver and analyzed in view of numerical accuracy. Here, two natural convection problems are solved to check the effect of the Rhie-Chow's method on numerical stability. And numerical diffusion from Rhie-Chow's method is studied by solving the inviscid flow around a circular cylinder.
