High order modeling of shocks and disturbances in compressible flows using WENO scheme

Abstract

Two new higher order version of WENO schemes are introduces and problems are solved to investigate problems containing shocks and disturbances in compressible flow. The solver is capable of solving conservation laws using WENO scheme of up to 7th order. The scheme is a recently developed version of the WENO-η-z method with a modified Global Smoothness Indicator (GSI) of 12th order of accuracy, aimed to decrease numerical dissipation over critical points. The code is primarily investigated trough solving several 1D and 2D problems, including the Sod’s shock tub, Lax’s problem, the Shu-Osher problem, which some are presented here as verification. The 2-D shock-bobble interaction and Richtmyer-Meshkov instability are solved as problems including shocks and disturbances, in which proposed methods are compared with both original WENO- η-z and two similarly modified methodes from recent literature. In these problems, the introduced scheme shows lower dissipation in comparison with the original versions, while having more acceptable stability and symmetry against other modifien versions.

Keywords

• high order scheme
• supersonic flow
• shock-disturbance
• numerical dissipation
• smoothness indicator