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.

Rarefaction waves in van der Waals fluids with an arbitrary number of degrees of freedom

“…Other work has shown that a single measurement of the density profile (as a function of distance) for an expanding 1D material can be used to infer the pressure as a function of density [20]. Previous work on hydrodynamic waves in generalized VDW fluids in the vicinity of the two-phase regime, but still above the critical point, showed the possible presence of rarefaction shockwaves, particularly for foils of finite thickness [12,[21][22][23]].…”

Characterization of rarefaction waves in van der Waals fluids

“…the structure and properties of molecular liquids, liquid metals and crystals, their freezing and melting, and their critical behaviors [20]. With three degrees of freedom, the VDW EOS also corresponds to a monatomic gas at low density and does not yield rarefaction shockwaves [16,18,[21][22][23]. Nevertheless, the quantitative application of the VDW EOS must be checked and several directly measurable quantities can help us confirm, improve or reject the VDW model.…”