Efficient discretization of pressure-correction equations on non-orthogonal grids

An alternative discretization of pressure-correction equations within pressure-correction schemes for the solution of the incompressible Navier-Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non-orthogonal grids. As against standard approaches, where the non-orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure-correction equation to correspond to 5-point or 7-point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non-orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure-correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure-correction equation should be solved in each pressure-correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger.