Comparison of iterative and direct solution methods for viscous flow calculations in body-fitted co-ordinates

The computational efficiency of iterative and direct solution methods in viscous flows calculated on curvilinear coordinate systems is studied for cases including a series of two-dimensional planar channels with progressive skewness of the grid system and a kidney-shaped channel. The iterative method convergence rate, less rapid than that of the direct method, decreases monotonically with increasing global mesh skewness and Reynolds number, while the direct method is seen as insensitive to these variables. It is shown that the increased complexity of the equations in curvilinear coordinates causes the storage requirements and cost per iteration of the direct method to be higher than in corresponding Cartesian coordinate methods. Therefore, increases in grid size increase CPU time and computer storage needs of the direct method more severely than the iterative method.