Nonlinear hydrodynamic waves: Effects of the equation of state

Abstract

The problem of the decay of an initial discontinuity (the Riemann problem) is studied for a substance with abnormal properties when the rarefaction waves get a shock form, whereas the compression waves become nonsharp with the width proportional to the distance traveled. Such a situation is inherent to matter in a near-critical thermodynamic state and is also met in many other physical systems. The behavior of pressure jumps is compared for the van der Waals equation of state and for its more realistic three-parametric modification. It is shown that the evolution of the rarefaction and compression waves is strongly dependent on the value of the fundamental gasdynamic derivative determined by the equation of state. We demonstrate that for some substances with abnormal properties both rarefaction and compression waves can keep a shocklike form for a long period of time after discontinuity decay.