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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media
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A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media

机译：各向异性和分段均质介质中弹性波传播的空间不连续Galerkin方法的统一变分框架

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摘要

We present a unified multidimensional variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Based on an elastic wave oriented formulation and using a tensorial formalism, the proposed framework allows a better understanding of the physical meaning of the terms involved in the discontinuous Galerkin method. The unified variational framework is written for first-order velocity-stress wave equations. An uncoupled upwind numerical flux and two coupled upwind numerical fluxes using respectively the Voigt and the Reuss averages of elastic moduli are defined. Two numerical fluxes that are exact solutions of the Riemann problem on physical interfaces are also developed and analyzed in the 1D case. The implemented solvers are then applied to different elastic media, especially to polycrystalline materials that present a particular case of piecewise homogeneous media. The use of the three upwind numerical fluxes, which only solve approximately the Riemann problem at element interfaces, is investigated. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们为空间不连续Galerkin方法在各向异性和分段均匀介质中传播弹性波提供了一个统一的多维变分框架。基于弹性波定向公式并使用张量形式，提出的框架可以更好地理解间断Galerkin方法中涉及的术语的物理含义。为一阶速度应力波方程编写了统一的变分框架。分别使用弹性模量的Voigt和Reuss平均值定义了未耦合的迎风数值通量和两个耦合的迎风数值通量。在一维情况下，还开发并分析了两个数值通量，它们是物理界面上黎曼问题的精确解。然后将实现的求解器应用于不同的弹性介质，尤其是呈现出分段均质介质的特殊情况的多晶材料。研究了三个迎风数值通量的使用，它们只能解决单元界面处的黎曼问题。 （C）2018 Elsevier B.V.保留所有权利。

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