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arXiv · 2106.14506

A direction preserving discretization for computing phase-space densities

David J. Chappell·Jonathan J. Crofts·Martin Richter·Gregor Tanner
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Abstract

Ray flow methods are an efficient tool to estimate vibro-acoustic or electromagnetic energy transport in complex domains at high-frequencies. Here, a Petrov-Galerkin discretization of a phase-space boundary integral equation for transporting wave energy densities on two-dimensional surfaces is proposed. The directional dependence of the energy density is approximated at each point on the boundary in terms of a finite local set of directions propagating into the domain. The direction of propagation can be preserved for transport across multi-component domains when the directions within the local set are inherited from a global direction set. The range of applicability and computational cost of the method will be explored through a series of numerical experiments, including wave problems from both acoustics and elasticity in both single and multi-component domains. The domain geometries considered range from both regular and irregular polygons to curved surfaces, including a cast aluminium shock tower from a Range Rover car.

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BibTeXRIS

David J. Chappell, Jonathan J. Crofts, Martin Richter, Gregor Tanner. 2021-06-28. A direction preserving discretization for computing phase-space densities. https://arxiv.org/abs/2106.14506

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