The Application of an Adaptive Upwind Unstructured Grid Solution Algorithm to the Simulation of Compressible Laminar Viscous Flows Over Compression Corners

Abstract

In this contribution, we use an adaptive unstructured grid algorithm for the solution of steady laminar compressible viscous flows over compression corners. The spatial discretisation is achieved by means of general assemblies of triangular or quadrilateral cells, while the temporal discretisation is accomplished in a fully implicit fashion. The unknowns are associated with the cell vertices [1,2] and a first order upwind algorithm results from the use of the flux difference splitting method of Roe [3]. A higher order extension is achieved by using the MUSCL concepts of van Leer [4]. This requires a monotonic linear reconstruction of the solution on a general unstructured grid and this is accomplished by the use of variational recovery [5] with the incorporation of the slope limiting [6]. The solution of the implicit equation system is obtained by a point implicit relaxation process.