Nonlinear entropy stable Riemann solver with heuristic logarithmic pressure augmentation for supersonic and hypersonic flows

The work devises heuristic logarithmic pressure augmentation to overcome shock instability encountered by the nonlinear entropy stable Riemann solver under supersonic and hypersonic flows. The entropy stable Riemann solver involves three key ingredients: entropy variable, entropy conservative flux and entropy dissipation. Based on the derivation of wave strengths within entropy dissipation, the reasonable domination of the logarithmic pressure diffusion jump on entropy wave is conducive to shock stability. Thus, the basic idea of this approach is to introduce the additional logarithmic pressure diffusion term. The heuristic logarithmic pressure sensor with tanh function is constructed to detect shock discontinuities and activate this logarithmic diffusion term. In addition, the nonlinear eigenvalues are slightly modified by the neighboring cell values. Then, numerical test cases demonstrate its high shock robustness and shear layer resolution with attractive application to supersonic and hypersonic flows.