On direction preserving discretizations for computing phase-space densities
On direction preserving discretizations for computing phase-space densities
复制标题
关于计算相空间密度的方向保持离散化
DOI：
10.1063/5.0162265
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Chappell D
中科院分区：
文献类型：
--
作者：
Chappell D
射线流方法是计算高频下复域中振声或电磁能量传输的一种有效工具。本文提出了二维表面波能密度传输的相空间边界积分方程的Petrov-Galerkin离散化方法。能量密度的方向依赖关系在边界上的每个点用传播到区域的有限局部方向集来近似。当局部集合内的方向从全局方向集合继承时，传播方向可以被保留以用于跨多组分域的传输。该方法的适用范围和计算成本将通过一系列的数值实验来探索，包括单分量和多分量区域中的声学和弹性波动问题。考虑的区域几何范围从规则和不规则多边形到曲面，包括路虎汽车上的铸造铝制防震塔。
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 multicomponent 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 multicomponent 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.