Implementation of a smoothing pressure correction approach to the pressure-correction equation in order to maintain the use of SIMPLEC algorithms on non-staggered grids

摘要

Date (1996) introduced a pressure-correction equation containing mass-conserving and smoothing pressure correction terms to solve the Navier-Stokes equations. The benefit of the smoothing terms is satisfying the stokes's relation which is often overlooked as well as overcoming the decoupling problem of the pressure-velocity fields, which renders it applicable to collocated (non-staggered) grids. His derivation relied on assumptions relevant to the SIMPLE algorithm (Caretto et al., 1972). Such assumptions are, unfortunately, not directly applicable to SIMPLEC procedures (van Doormaal and Raithby, 1984). The main purpose of this paper is to extend the pressure-correction equation proposed by Date (1996) to SIMPLEC algorithms.