Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes

Hypersonic heating computations are still challenging due to difficulties in “(A) robust capturing of shockwaves” and “(B) accurate prediction of heating”. Based on our numerical survey for (A), we found that the dissipation inside the numerical shock wave structure (where no physical or mathematical explanation is valid) must be proportional to Mach number, in contrast to Mach independent dissipation provided by conventional AUSM fluxes. Then, we developed schemes that have those two properties above by combining (a) a proposed pressure flux (having Mach-proportional dissipation within numerical shock), and (b) a mass flux of an all-speed AUSM-family scheme (SLAU, AUSM+-up or LDFSS2001). The new schemes, called “SLAU2”, “AUSM+-up2”, and “LDFSS2001-2”, are applied to numerical tests, and their desired performances are demonstrated for a wide spectrum of Mach numbers, including hypersonic heating (for the latter two schemes), a low speed flow, and 3D aerodynamic applications.