Grid influence on upwind schemes for the Euler and Navier-Stokes equations

The grid influence on the standard Roe's upwind scheme in two space dimensions is investigated. It is shown that inaccurate solutions can be obtained even in smooth flow regions and even with regularly structured triangular meshes. Some numerical analyses and various inviscid and viscous computations are conducted to provide a better understanding of this behavior. High-order reconstructions together with the standard scheme are shown to give only limited improvements. A grid-independent upwind scheme based on a five-wave model has been tested and has shown some potential in improving the situation.