Dissipative Waves in Real Gases

TL;DR

This paper analyzes shock wave solutions in a van der Waals fluid, deriving an amplitude equation with nonlinearities, dissipation, and diffraction, and explores how real gas effects influence shock characteristics.

Contribution

It introduces an asymptotic amplitude equation for unsteady 2D flow of a van der Waals fluid, incorporating nonlinearities, dissipation, and diffraction, with exact solutions via symmetry reduction.

Findings

Real gas parameters affect shock shape and strength.

Wave profiles experience distortion and steepening leading to shock formation.

Shock decay behavior is influenced by van der Waals parameters.

Abstract

In this paper, we characterize a class of solutions to the unsteady 2-dimensional flow of a van der Waals fluid involving shock waves, and derive an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities including dissipation and diffraction. We exploit the theory of nonclassical symmetry reduction to obtain some exact solutions. Because of the nonlinearities present in the evolution equation, one expects that the wave profile will eventually encounter distortion and steepening which in the limit of vanishing dissipation culminates into a shock wave; and once shock is formed, it will propagate by separating the portions of the continuous region. Here we have shown how the real gas effects, which manifest themselves through the van der Waals parameters $\tilde{a}$ and $\tilde{b}$ influence the wave characteristics, namely the shape, strength, and decay behavior of shocks.