Solution of the Euler Equations on Unstructured and Adaptive Meshes

Abstract

The present report deals with a numerical scheme for solving the two-dimensional Euler equations on unstructured grids, based on a finite-volume discretization. This kind of discretization was first proposed by Jameson, Schmidt and Turkel. Using central differencing, additionally to the convective fluxes artificial dissipative fluxes are required in the explicit numerical scheme to guarantee a stable solution procedure. The different evaluations of the dissipative operator on unstructured grids described in the literature are tested and discussed. For sub- and transonic flow cases a good agreement with results achieved by flow solvers on quadrilateral meshes is shown. Subsequently, the extension of the numerical method using adaptive unstructured meshes is presented. In the present method auxiliary points are generated during the solution process in order to get a mesh refinement in regions of the flowfield, where high gradients of the flow-variables occur. Some results for sub- and transonic flow-problems are treated and discussed.