Fundamental models in nonlinear acoustics part I. Analytical comparison

TL;DR

This paper analyzes fundamental nonlinear acoustic models, rigorously justifies classical equations like Kuznetsov and Westervelt, and sets the stage for numerical validation in subsequent work.

Contribution

It provides a rigorous derivation and comparison of key nonlinear damped wave equations in acoustics, clarifying their relationships and validity.

Findings

Justification of Kuznetsov and Westervelt equations as limits

Hierarchy of nonlinear damped wave models derived

Theoretical foundation for numerical comparisons

Abstract

This work is concerned with the study of fundamental models from nonlinear acoustics. In Part~I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In particular, a rigorous justification of two classical models, the Kuznetsov and Westervelt equations, retained as limiting systems for consistent initial data, is given. Numerical comparisons that confirm and complement the theoretical results are provided in Part~II.