Pressure-equation-based SLAU2 for oscillation-free, supercritical flow simulations

An AUSM (Advection-Upstream-Splitting-Method) family flux function SLAU (Simple Low-dissipation AUSM) 2, developed by Kitamura, K., and Shima, E. [J. Comput. Phys. 245:62-83, 2013], has been modified to give a direct, but non-conservative, solution for the pressure by solving the pressure equation, instead of the energy equation. Numerical examples demonstrate that pressure errors known for conventional methods are successfully avoided without relying upon higher-order schemes or artificial diffusion, even in a multi-dimensional viscous flow. In addition, the present extension is applicable to a different AUSM family flux. These encourage us to further apply the present method to practical problems involving complex geometries.