Toward an improved wall treatment for multiple-correction k-exact schemes

Abstract

Improved wall boundary treatments are investigated for a family of high-order Godunovtype finite volume schemes based on k-exact polynomial reconstructions in each cell of the primitive variables, via a successive corrections procedure. We focus more particularly on the 1-exact and 2-exact schemes which offer a good trade-off between accuracy and computational efficiency. In both cases, the reconstruction stencil needs to be extended to the boundaries. Additionally, information about wall curvature has to be taken into account, which is done by using a surface model based on bicubic Bézier patches for the walls. The performance of the proposed models is presented for two compressible cases, namely the inviscid flow past a Gaussian bump and the viscous axisymmetric Couette flow.