A streamline-upwind/petrov-galerkin formulation for supersonic and hypersonic flow simulations

Abstract

In this talk, we deal with a simplified version of chemically reactive multi-species hypersonic flow around a cylinder. For this purpose, it is assumed that the flow environment only consists of nitrogen gas (N$_{2}$), and no chemical reaction takes place in the flow field. Furthermore, the flow is assumed to be inviscid. A stabilized method is needed to prevent the numerical oscillations caused by the advection terms in the governing equations. Beyond that, a shock-capturing method is needed to obtain good solution profiles at the shocks. In this study, we use the compressible-flow Streamline-Upwind/Petrov-Galerkin method, complemented with the YZβ shock-capturing. The zero-normal-velocity condition on the cylinder is enforced weakly. Numerical simulations are carried out in the FEniCS ecosystem for both supersonic and hypersonic freestream conditions.