Discrete flow mapping: transport of phase space densities on triangulated surfaces
Discrete flow mapping: transport of phase space densities on triangulated surfaces
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DOI：
10.1098/rspa.2013.0153
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发表时间：
2013-07-08
影响因子：
3.5
通讯作者：
Sondergaard, Niels
中科院分区：
文献类型：
--
作者：
Chappell, David J.;Tanner, Gregor;Sondergaard, Niels
高频线性波场的能量分布通常用流动或输运方程来模拟，其中射线动力学由相空间中的哈密顿向量场给出。应用出现在水下和室内声学，振动声学，地震学，电磁学和量子力学。基于一般守恒定律的相关流动问题用于天气预报或分子动力学模拟。这些流动方程的解往往是大规模的、复杂的和高维的，这给数值近似方法带来了巨大的挑战。本文提出了一种有效的和广泛适用的方法，称为离散流映射，解决这类问题的三角化表面。本文介绍了在结构动力学中的一个应用，确定了一个铸铝车身部件的振动声响应。
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, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in 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 vibroacoustic response of a cast aluminium car body component, is presented.