Pseudospectral approximation compared with control volume formulation and finite differences- some test cases

The paper presents comparison of the pseudospectral method with low-order approximation for two test cases. The first test case is quasi one-dimensional supersonic flow through converging-diverging nozzle for which exact solution exists. The comparison of the error of pseudospectral approximation and upwind finite-differences using Steger-Warming flux splitting method shows high accuracy of the pseudospectral method even for few collocation points. The same conclusion is formulated for the second test case, namely incompressible flow in two-dimensional driven cavity solved by control volume formulation with modified QUICK upwinding scheme and SIMPLEC algorithm for pressure correction. As usually conclusions concerning accuracy of numerical methods are flow case dependent, but the two examples shown give some idea about the accuracy and resolution of spectral approximation versus standard CFD schemes.