Solving the stationary Liouville equation via a boundary element method
Solving the stationary Liouville equation via a boundary element method
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DOI：
10.1016/j.jcp.2012.10.002
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发表时间：
2013-02-01
影响因子：
4.1
通讯作者：
Tanner, Gregor
中科院分区：
文献类型：
--
作者：
Chappell, David J.;Tanner, Gregor
在高频极限下，线性波场的能量分布通常用相空间中的流动或传输方程来近似。求解瞬态问题和稳态问题中的流动方程的常用技术是射线追踪和水平集方法。在预测复杂工程结构的振动声学响应的背景下，统计能量分析等相关方法或其变体已得到广泛应用。我们提出了一种基于稳态刘维尔方程的边界元公式求解复杂多组分结构输运方程的新方法。该方法是作者最近推出的动态能量分析技术的改进版本。它在标准统计能量分析和全光线追踪之间进行插值，并将这两种方法作为限制情况。我们证明，该方法可用于有效地处理复杂的大规模问题，与基础波动方程的精确解相比，可以给出能量分布的良好近似值。 (C) 2012 Elsevier Inc. 保留所有权利。
Energy distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations in both time dependent and stationary problems are ray tracing and level set methods. In the context of predicting the vibro-acoustic response of complex engineering structures, related methods such as Statistical Energy Analysis or variants thereof have found widespread applications. We present a new method for solving the transport equations for complex multi-component structures based on a boundary element formulation of the stationary Liouville equation. The method is an improved version of the Dynamical Energy Analysis technique introduced recently by the authors. It interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. We demonstrate that the method can be used to efficiently deal with complex large scale problems giving good approximations of the energy distribution when compared to exact solutions of the underlying wave equation. (C) 2012 Elsevier Inc. All rights reserved.