Numerical study of dynamic phase transitions in shock tube

Shock tube problem of a van der Waals fluid with a relaxation model was investigated. In the limit of relaxation parameter tending towards zero, this model yields a specific Riemann solver. Relaxing and relaxed schemes were derived. For an incident shock in a fixed tube, numerical simulations show convergence toward the Riemann solution in one space dimension. Impact of parameters was studied theoretically and numerically. For certain initial shock profiles, nonclassical reflecting wave was observed. In two space dimensions, the effect of curved wave fronts was studied, and some interesting wave patterns were exposed.