Discrete flow mapping: transport of phase space densities on triangulated surfaces

TL;DR

This paper introduces discrete flow mapping, an efficient numerical method for solving high-dimensional flow equations on triangulated surfaces, with applications in vibro-acoustics and structural dynamics.

Contribution

The paper presents a novel discrete flow mapping technique that effectively approximates phase space densities on triangulated surfaces for various high-frequency wave applications.

Findings

Successfully applied to vibro-acoustic response of a car body component

Demonstrated efficiency and broad applicability of the method

Addresses large-scale, complex flow problems in multiple fields

Abstract

Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented.