On energy preserving high-order discretizations for nonlinear acoustics

TL;DR

This paper develops high-order energy-preserving numerical methods for solving the Westervelt equation in nonlinear acoustics, ensuring accurate and stable simulations by systematically discretizing the problem with Galerkin methods.

Contribution

It introduces a systematic approach to construct exact energy-preserving high-order discretizations for the Westervelt equation, linking them to existing methods.

Findings

Exact energy-preserving methods of arbitrary order are derived.

Efficient implementation strategies are discussed.

The relation to other common numerical methods is analyzed.

Abstract

This paper addresses the numerical solution of the Westervelt equation, which arises as one of the model equations in nonlinear acoustics. The problem is rewritten in a canonical form that allows the systematic discretization by Galerkin approximation in space and time. Exact energy preserving methods of formally arbitrary order are obtained and their efficient realization as well as the relation to other frequently used methods is discussed.