Abstract
We present a four-velocity kinetic model of van der Waals fluids. Although, from the physical point of view this model is very simple, mathematically it is quite complicated. Due to this complexity we performed various simplifications, which are also presented. We look for traveling wave solutions for these simplified versions. A discussion of the types of the states of rest is presented. We pay some attention to the monotonicity of the density component of the traveling wave. Finally, we compare the model's kinetic and hydrodynamic shock wave structures. The new feature is that kinetic effects alone are unable to kill the artificial phenomenon of impending shock splitting.
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Kaźmierczak, B., Piechór, K. Shock waves by a kinetic model of van der Waals fluids. ARI 51, 203–215 (1999). https://doi.org/10.1007/s007770050055
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DOI: https://doi.org/10.1007/s007770050055