ANALYSIS OF PRESSURE-VELOCITY COUPLING ON NONORTHOGONAL GRIDS

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Abstract
Extension of the SIMPLE pressure-velocity coupling algorithm to nonorthogonal grids results in a very complex pressure-correction equation (e.g., a 9-point computational molecule in a two-dimensional case, a 19-point.computational molecule in a three-dimensional case) The usual practice is therefore to further simplify this equation by neglecting the effect of nonorthogonality on the mass flux corrections, thus reducing the computational molecule to 5 or 7 points The paper analyzes the performance of the simplified and full pressure-correction equations when the grid nonorthogonality becomes appreciable. It is demonstrated here that the efficiency of the simple coupling algorithm is not affected by the grid nonorthogonality, provided that no additional simplifications are introduced in the pressure-correction equation. However, the algorithm with the simplified equation becomes inefficient when the angle between grid lines approaches 45° and it usually fails to converge for angles below 30°. The problem of solving the full 9-point pressure-correction equation is best dealt with by employing the biconjugate gradient solver, which proved to be the most robust one in test calculations carried out in this study.