High-Order Finite-Di erence Shock-Fitting Schemes for Direct Numerical Simulation of Hypersonic Boundary-Layer Receptivity to Free-Stream Disturbances

Direct numerical simulation of the receptivity of hy-personic boundary-layers to freestream disturbances requires high-order accurate numerical methods to resolve a wide range of time and length scales. Traditional second-order nite diierence schemes do not have an adequate accuracy level for the direct numerical simulation. In addition, hypersonic ow simulation needs to resolve unsteady bow shocks and to include stii thermo-chemical nonequilibrium source terms. This paper presents new high-order (up to sixth order) upwind nite diierence shock tting schemes for the direct numerical simulation of hypersonic boundary layers with real gas eeects. The current methods include a simple shock tting formulation for high-order discretization, new upwind high-order compact and explicit nite diierence schemes, and third-order semi-implicit Runge-Kutta schemes to compute stii nonequilibrium thermo-chemical source terms. The numerical methods have been tested in a one-dimensional linear wave equation and a steady two-dimensional hy-personic ow over a parabola. The preliminary results show that the current shock-tting methods are accurate and robust.