Assessment of SLAU2 and other flux functions with slope limiters in hypersonic shock-interaction heating

• Flux functions, limiters, and reconstructed variables all affect shock anomalies.
• AUSM+-up and AUSMPW+ improve shock-robustness as the spatial accuracy increases.
• On the other hand, SLAU2 and Hänel tend to do the opposite.
• SLAU2, AUSM+-up, or AUSMPW+ with κ = –1, minmod-MUSCL (primitive) is recommended.
• Mass flux preservation is added to the element of “Hypersonic CFD Tips.”

Roles of flux functions (such as SLAU2 Kitamura and Shima, 2013), limiters, and reconstructed variables are thoroughly investigated in problems related to hypersonic heating issues, i.e., shock anomalous solutions (e.g., carbuncle phenomenon) and shock-interaction heating. Through numerical tests comparing those different combinations, it is revealed that each of those factors has great impacts on the solutions at almost the same level. In particular, flux functions having at most one intermediate cell at the captured shock (e.g., AUSM+-up) show improved robustness against shock anomalies as the spatial accuracy increases, whereas those containing a few cells to represent the shock (e.g., SLAU2) tend to do the opposite. Among many possible combinations, SLAU2, AUSM+-up, or AUSMPW+ along with κ = -1, minmod-limited monotone upstream-centered schemes for conservation laws (MUSCL) interpolation for primitive variables show acceptable performance in the present study, as confirmed by the severe Type IV shock-interaction heating problem. In addition, conservation of mass flux across a shockwave is proven to be essential in accurate heating computations, indicating a possible, further modification of SLAU2.