Improvement of upwind schemes with the Least Square method in the DLR TAU Code

Accuracy investigations for upwind schemes in the framework of a node based and cell centered discretisation for the Euler and Navier Stokes equation on unstructured hybrid grids are presented. A crucial factor for the accuracy of the upwind discretisation is the used computation of gradients. The Least-Square approach will be investigated in comparison to the well known Green-Gauss algorithm. Numerical results are obtained for subsonic inviscid and subsonic turbulent flows around airfoils. The frequently used central scheme for applications of subsonic to transonic flows will be used as a reference for the results. In case of upwind discretisations the cell centered formulation in combination with the Least-Square reconstruction provides the most accurate results.