A finite volume scheme with shock fitting for the steady Euler equations
Analysis of two alternative finite volume formulations, in respect of accuracy on non-uniform meshes and number of spurious modes, leads to a preference for the more compact cell vertex scheme over the cell centre scheme. The resulting equations are solved iteratively by using a Lax- Wendroff procedure as a smoother for a multigrid algorithm: then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero - except at shocks. At shocks the residuals should not be zero and a shock-fitting procedure is introduced to avoid this inconsistency. Sharp, accurate solutions on a relatively coarse mesh are obtained for a channel flow problem in which the Zierep singularity is displayed, and for the NACA 0012 aerofoil.
scientific article; zbMATH DE number 4072605
scientific article