Abstract This research work presents, within a unified and wave oriented variational framework, systematic development of upwind numerical fluxes for the space discontinuous Galerkin methods to model elastic wave propagation in multidimensional anisotropic media with discontinuous material properties. Both first-order velocity–stress and velocity–strain wave formulations are considered. The proposed approach allows the derivation of upwind numerical fluxes in a well structured and hierarchical way according to the degree of inhomogeneity across a physical interface. The numerical fluxes that are exact solutions of a relevant Riemann problem defined at a physical interface are obtained. The developed explicit and intrinsic tensorial expressions of upwind numerical fluxes in multidimensional case allow a better understanding and analysis of the physical meaning of involved terms. As numerical applications, an example with a physical interface separating two materials, one anisotropic and the other isotropic, and an example of polycrystalline material that presents a particular case with a larger number of physical interfaces, are considered. The proposed numerical fluxes are numerically investigated and validated.

中文翻译：

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空间不连续伽辽金法应用于具有物理界面的各向异性和非均质介质中弹性波传播的逆风数值通量的系统发展

摘要 本研究工作在统一的面向波浪的变分框架内，系统地开发了空间不连续伽辽金方法的逆风数值通量，以模拟具有不连续材料特性的多维各向异性介质中的弹性波传播。一阶速度-应力和速度-应变波公式都被考虑。所提出的方法允许根据物理界面上的不均匀程度以结构良好和分层的方式推导逆风数值通量。获得作为在物理界面定义的相关黎曼问题的精确解的数值通量。在多维情况下开发的逆风数值通量的显式和内在张量表达式允许更好地理解和分析所涉及术语的物理含义。作为数值应用，考虑了物理界面分隔两种材料（一种是各向异性的，另一种是各向同性的）的示例，以及呈现具有大量物理界面的特定情况的多晶材料的示例。对提议的数值通量进行了数值研究和验证。