A third order correction to the Helmholtz equation

Abstract

In this work we derive a third order correction to the classical Helmholtz equation. Starting from non‐linear Euler equations and using asymptotical analysis we get a decoupled system of linear, Helmholtz type equations, which are written in terms of the acoustical pressure functions. We present also a rather simple concept of the boundary conditions. Also numerical results and accompanying difficulties are discussed and presented.

Remiantis Oilerio lygtimis ir asimptotine analize gautas Helmholco lygties trečiosios eiles patikslinimas. Akustiniam slegiui gauta Helmholco tipo lygtis bei jai išvestos salygos. Pateikti skaitinio modeliavimo rezultatai.

Key words:

• non‐linear acoustics
• Euler equations
• asymptotic analysis
• scaling
• Helmholtz type equation
• pressure
• displacement
• Lagrangian coordinates
• non‐homogeneous Neumann boundary conditions
• radiation boundary conditions