Transport of phase space densities through tetrahedral meshes using discrete flow mapping
Transport of phase space densities through tetrahedral meshes using discrete flow mapping
复制标题
使用离散流映射通过四面体网格传输相空间密度
DOI：
10.1016/j.jcp.2016.10.019
复制
发表时间：
2017-01-01
影响因子：
4.1
通讯作者：
Tanner, Gregor
中科院分区：
文献类型：
--
作者：
Bajars, Janis;Chappell, David J.;Tanner, Gregor
离散流映射是最近提出的一种基于射线的确定复杂组合结构中波浪能量分布的有效方法。使用光线传递算子的有限维近似，通过多边形网格单元沿光线轨迹传输波能量密度。通过这种方式，可以将该方法视为定义在网格化曲面上的平滑光线跟踪方法。许多应用都需要求解三维波的能量分布，如室内声学、水下声学和电磁空腔问题。在这项工作中，我们通过在四面体网格中传播波的能量密度，将离散流映射扩展到三维区域。利用四面体网格单元的几何简单性，使用解析和光谱精确的数值积分的混合来有效地计算光线传递算子。通过位置坐标中四面体面上的低阶局部近似和动量空间中的高阶多项式展开，解决了如何在保持合理计算代价的情况下在相空间中选择合适的基近似这一重要问题。(C)2016 Elsevier Inc.保留所有权利。
Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space. (C) 2016 Elsevier Inc. All rights reserved.