Bulgakova N M, Burakov I M
Institute of Thermophysics SB RAS, prosp. Lavrentyev 1, 630090 Novosibirsk, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036303. doi: 10.1103/PhysRevE.70.036303. Epub 2004 Sep 13.
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.
研究了具有异常性质的物质在初始间断（黎曼问题）衰减时的问题，此时稀疏波呈激波形式，而压缩波变得不尖锐，其宽度与传播距离成正比。这种情况是近临界热力学状态下物质所固有的，在许多其他物理系统中也会出现。比较了范德瓦尔斯状态方程及其更符合实际的三参数修正形式下压力跃变的行为。结果表明，稀疏波和压缩波的演化强烈依赖于由状态方程确定的基本气体动力学导数的值。我们证明，对于某些具有异常性质的物质，在间断衰减后，稀疏波和压缩波都能在很长一段时间内保持激波状形式。
