Six Convective Difference Schemes on Different Grid Systems for Fluid Flow and Heat Transfer with SIMPLE Algorithm

INTRODUCTIONThe evaluations of the dependent variables at thecell faces are sensitive to the aChievement of accurate and economical numerical solutions of fluid flowin the finite volume method with both staggered andcollocated grids, and many difference schemes wereproposed for this purpose during the past decades.Among them there are several ones being widely used,discussed and investigated concerning their numerical performance and/or char.cteristics1-5]. Theseschemes are central diffe…

Six convective difference schemes on different grid systems for fluid flow and heat transfer with SIMPLE algorithm

Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow and heat transfer based on the finite volume method using staggered and Rhie-Chow's momentum interpolation collocated grids, the second part contains the comparative computations being conducted on Rhie-Chow's momentum interpolation collocated grid and Thiart's finite difference scheme based nonstaggered grid. Three 3-D cases that have analytical or benchmark solutions are adopted. For the first part, the results of computations indicate that, all the six schemes have the same numerical accuracy when the diffusion term is predominant. With the increase of convection, the FUDS, HDS and PLDS almost have the same accuracy in two of those grid systems, while the SUDS and QUICK have higher accuracy than the former. The accuracy of CDS is something in between. For the same under-relaxation factors and convergence criterion, the convergence rate of each scheme on those two grid systems are nearly equal with that on the staggered grid being a little bit faster. For QUICK and CDS, smooth, non-oscillating solutions can be obtained even when local Peclet number may be as large as 31.2-31.3. For the second part, it is concluded that simplified collocated grid system is preferable from numerical accuracy, grid Peclet number limit, sensitivity to the underrelaxation factor and the freedom in choosing finite difference scheme for convection term.