Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage

TL;DR

This paper derives a new dispersion relation for unstable sound waves in a non-equilibrium gas, analyzes their stability boundaries, and investigates their nonlinear evolution leading to shock wave formation using advanced numerical simulations.

Contribution

It introduces a novel dispersion equation for non-equilibrium media and explores the nonlinear development of sound wave instability with high-performance numerical methods.

Findings

Identified stability regions for sound waves in non-equilibrium gases.

Validated numerical simulations against linear perturbation theory.

Demonstrated shock wave formation at nonlinear stages.

Abstract

A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.