Improving the treatment of near-wall regions for multiple-correction k-exact schemes. (15th March 2019) - Menasria, A.; Brenner, P.; Cinnella, P.
Highlights: A family of high-order k -exact reconstruction schemes was provided. Close to walls, a decrease of accuracy is observed with the present schemes. A new wall treatment is applied to the 1-exact and 2-exact reconstructions. It is based on three improvements: curvature, low-Mach correction, stencil enrichment. The strategy is applied on two inviscid cases, and gains in accuracy are observed. Abstract: A high-order wall treatment is investigated for a family of high-order Godunov-type finite volume schemes based on k -exact polynomial reconstructions of the primitive variables in each cell via a successive-corrections procedure of the derivatives. We focus more specifically on the 1-exact and 2-exact schemes, which offer a good trade-off between accuracy and computational efficiency. The modifications are threefold. First, wall curvature is taken into account by introducing a new model of the wall surfaces based on bicubic Bézier patches. A low-Mach correction is then introduced in the Riemann solver to retrieve accuracy in near-wall regions characterized by low velocity. Finally, the reconstruction stencil is enriched at the boundaries. The benefits of these numerical treatments are studied for two inviscid test cases, namely the flow past a Gaussian bump and the subsonic flow around a circular cylinder.