General Formulations for Rhie-Chow Interpolation

Abstract

In this paper, general formulations for Rhie-Chow interpolation on co-located grid are derived. Unlike the standard Rhie-Chow interpolation, the general formulations are applicable for any flow conditions. It has observed that the original momentum-based interpolation due to Rhie and Chow has serious deficiency, such as under-relaxation factor dependence, failure to suppress saw-tooth pressure solutions with small time step size for unsteady state problems and wrong solutions or divergence with discontinuities. Thus the derivation of Rhie-Chow interpolation is first recalled, then the errors of numerical discretization are analyzed, finally, new formulations and some improvements are given.

Simulation of Instabilities in Liquid Metal Batteries

“…It was implemented e.g. in buoyantBoussinesqPimpleFoam as proposed by Zhang and Zhao [10]. In the corrector step, the velocity-independent Lorentz force is interpolated to the cell faces and added to the velocity flux term.…”

Modeling and simulation of conditionally volume averaged viscoelastic two‐phase flows

“…Furthermore, in order to smooth out the pressure field, which is necessary in the numerical procedure, 31 we will make use of a modified pressure p d by separating out the hydrostatic pressure, 2 qg Á x, where x is the position vector and q 5 a u q u 1 1 2 a u À Á q x . The momentum equation for quiescent fluids and flat interfaces is…”

On the hyperbolicity of the two-fluid model for gas–liquid bubbly flows

“…The solver implements a pressure-based solution algorithm designed for a co-located grid arrangement [52]. The checkerboard effect is avoided by means of an improved formulation of the Rhie-Chow interpolation [53,54]. The buoyancy term is incorporated in the pressure, and other contributions to the momentum exchange term are treated as fluxes, at cell faces [54].…”

“…The checkerboard effect is avoided by means of an improved formulation of the Rhie-Chow interpolation [53,54]. The buoyancy term is incorporated in the pressure, and other contributions to the momentum exchange term are treated as fluxes, at cell faces [54]. The drag contribution to the momentum exchange term is treated with the partial elimination procedure [55][56][57].…”