Numerical simulation of a one-dimensional shock tube problem at supercritical fluid conditions

The numerical computation of supercritical fluid flows is extremely challenging because of the complexity of the physical processes and the disparity of the space and time scales involved. Supercritical fluids exhibit large density fluctuations especially very close to the critical region. In this region, the perfect gas law is no longer valid and has to be replaced by a specific equation of state (EoS) as, for instance, the Altunin and Gadetskii EoS. In the present work, the problem of choosing a suitable numerical scheme for dense gas flow computations in a shock tube is addressed. In particular, the extension of the classical Roe’s scheme to real gas flows is used and its performance is evaluated by comparing with the analytical profile of the dimensionless density obtained by Sod in the shock tube problem. The application of this numerical implementation near the critical region of the fluid gives significant differences compared to gas dynamics and shows a relevant behaviour of the compressibility variation and localises an important gradient of temperature in the shock tube.