Accelerated convergence of the numerical simulation of incompressible flow in general curvilinear co‐ordinates by discretizations on the double‐staggered grids

Abstract

AbstractThe convergence rate of a methodology for solving incompressible flow in general curvilinear co‐ordinates is analyzed. Double‐staggered grids (DSGs), each defined by the same boundaries as the physical domain, are used for discretization. Both grids are MAC quadrilateral meshes with scalar variables (pressure, temperature, etc.) arranged at the center and the Cartesian velocity components at the middle of the sides of the mesh cells. The problem was checked against benchmark solutions of natural convection in a squeezed cavity, heat transfer in concentric horizontal cylindrical annuli, and a hot cylinder in a duct.Poisson's pressure‐correction equations that arise from the SIMPLE‐like procedure are solved by several methods: successive overrelaxation, symmetric overrelaxation, modified incomplete factorization preconditioner, conjugate gradient (CG), and CG with preconditioner. A genetic algorithm was developed to solve problems of numerical optimization of SIMPLE‐like calculation time in a space of iteration numbers and relaxation parameters. The application provides a means of making an unbiased comparison between the DSGs method and the widely used interpolation method. Furthermore, the convergence rate was demonstrated by application to the calculation of natural convection heat transfer in concentric horizontal cylindrical annuli. Calculation times when DSGs were used were 2–10 times shorter than those achieved by interpolation. With the DSGs method, calculation time increases slightly with increasing non‐orthogonality of the grids, whereas an interpolation method calls for very small iteration parameters that lead to unacceptable calculation times. Copyright © 2007 John Wiley & Sons, Ltd.