zbMATH — the first resource for mathematics

Improvements to incompressible flow calculation on a nonstaggered curvilinear grid. (English) Zbl 0694.76019
Summary: The semi-implicit method for pressure-linked equations (SIMPLE) algorithm of C. M. Rhie and W. L. Chow [AIAA J. 21, 1525-1532 (1983; Zbl 0528.76044)] for flow problems on nonstaggered curvilinear grids is extended, and a SIMPLE-revised (SIMPLER) algorithm is formulated on nonstaggered curvilinear grids. In addition, a new algorithm, SIMPLE- modified (SIMPLEM), is formulated. The performance of these three algorithms is examined through two test problems (driven flow in a cavity and flow in a sudden expansion). The integral form of the continuity equation is shown to be not satisfied in the SIMPLE formulation. In the SIMPLER formulation, the residuals of the momentum equation do not decrease to acceptably low values. The SIMPLEM algorithm shows reasonably good convergence behaviour and is superior to both the SIMPLE and SIMPLER algorithms. On the basis of these comparisons, the SIMPLEM algorithm is recommended for use in nonstaggered curvilinear meshes.

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M99 Basic methods in fluid mechanics
76F99 Turbulence
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
Full Text: DOI