For a clear and comprehensive opinion on segregated SIMPLE algorithm in the area of computational fluid dynamics (CFD) during liquid processing of materials, the most significant developments on the SIMPLE algorithm and its variants are briefly reviewed. Subsequently, some important advances during last 30 years serving as increasing numerical accuracy, enhancing robustness and improving efficiency for Navier–Stokes (N-S) equations of incompressible fluid flow are summarized. And then a so-called Direct-SIMPLE scheme proposed by the authors of present paper introduced, which is different from SIMPLE-like schemes, no iterative computations are needed to achieve the final pressure and velocity corrections. Based on the facts cited in present paper, it conclude that the SIMPLE algorithm and its variants will continue to evolve aimed at convergence and accuracy of solution by improving and combining various methods with different grid techniques, and all the algorithms mentioned above will enjoy widespread use in the future.

Development of SIMPLE-Like Algorithms for Incompressible Navier-Stokes Equations in Liquid Processing of Materials

Six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow based on the finite difference method were systematically investigated. The computations were performed on the collocated grid system. Effects of accuracy, stability, and convergence characteristics of the schemes on the solutions of the Navier Stokes equations were analyzed respectively. The results indicate that, all schemes have the same effects on computational efforts when the diffusion term is predominant on collocated grid. With the increase of convection, or the convection to be dominant, the FUDS, HDS and PLDS have almost the same accuracy on the two grids, while the SUDS and QUICK have higher accuracy than the formers and the CDS is in the middle. For the same under relaxation parameters of velocity and pressure and the same convergence criterion, the convergence rates of each scheme are nearly equal.

Effects of Various Difference Schemes on Collocated Grid Systems

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Effects of Various Difference Schemes on Collocated Grid Systems