Application of Essentially Nonoscillatory Hypersonic Shock-Shock Interference Schemes to Unsteady Heating Problems

This paper applies the high-order finite-volume essentially nonoscillatory (ENO) schemes to unsteady hypersonic shock-shock interference heating on a circular cylinder. Compared with most of the current second-order numerical methods, which usually are not uniformly accurate, the EN0 schemes are able to achieve uniformly high-order accuracy with essentially no oscillation in simulating the aerodynamics of hypersonic flows. Timeaccurate high-resolution numerical solutions of the Navier-Stokes equations for a type IV hypersonic shock-wave interference heating problem have been obtained by using the third-order accurate EN0 scheme in time and space. The computational results show that the interference-heating flow is inherently unsteady and the inherent unsteadiness is the result of interaction among the unsteady shear layers, impinging jet, and bow shock waves. The numerical results of the surface heating rates and pressure distribution compare well with experimental measurements. Meanwhile, implicit EN0 schemes for the Navier-Stokes equations are also tested in supersonic boundary layer and shockhoundary-layer interaction flow computations.