On the structure of isothermal acoustic shocks under classical and artificial viscosity laws: Selected case studies

TL;DR

This paper investigates the structure of isothermal acoustic shocks under various viscosity laws using analytical and numerical methods, deriving shock properties and bounds on Mach numbers for different viscosity models.

Contribution

It provides new analytical and numerical insights into shock structure under multiple viscosity laws, including explicit expressions for shock thickness and asymmetry.

Findings

Derived expressions for shock thickness and asymmetry for each viscosity law

Computed upper bounds on Mach numbers for isothermal flow

Validated analytical results with numerical simulations

Abstract

Assuming Newton's law of cooling, the propagation and structure of isothermal acoustic shocks are studied under four different viscosity laws. Employing both analytical and numerical methods, 1D traveling wave solutions for the velocity and density fields are derived and analyzed. For each viscosity law considered, expressions for both the shock thickness and the asymmetry metric are determined. And, to ensure that isothermal flow is achievable, upper bounds on the associated Mach number values are derived/computed using the isothermal version of the energy equation.