Approximation of a compressible Navier-Stokes system by non-linear acoustical models

TL;DR

This paper analyzes how non-linear acoustical models like Kuznetsov, NPE, and KZK approximate solutions of the compressible Navier-Stokes system, using a corrector approach to validate their accuracy.

Contribution

It introduces a corrector-based derivation method that rigorously justifies the approximation of compressible Navier-Stokes solutions by non-linear acoustical models.

Findings

The corrector approach improves the derivation accuracy.

Validation provided specifically for the KZK equation.

Models are shown to approximate the Navier-Stokes system effectively.

Abstract

We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a com-pressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case.