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Abstract <p>The grid-characteristic method on regular structured meshes is combined with a discontinuous Galerkin method on tetrahedral meshes to solve the direct problem of three-dimensional elastic wave propagation through a geological medium consisting of four linear elastic layers with different parameters and arbitrary curved boundaries. The numerical methods are matched using a special algorithm taking into account the features of the transition from unstructured tetrahedral to regular structured meshes in three-dimensional space. A comparative convergence analysis of the combined method and the grid-characteristic method on curvilinear structured meshes is performed depending on the step sizes in spatial directions. The wave field of the velocity magnitude is obtained for a perturbation propagating from the source.</p>

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Grid-Characteristic Method Combined with Discontinuous Galerkin Method for Simulation of Wave Propagation through Linear Elastic Media in the Three-Dimensional Case

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. V. Favorskaya,
  • I. B. Petrov,
  • A. A. Kozhemyachenko

摘要

Abstract

The grid-characteristic method on regular structured meshes is combined with a discontinuous Galerkin method on tetrahedral meshes to solve the direct problem of three-dimensional elastic wave propagation through a geological medium consisting of four linear elastic layers with different parameters and arbitrary curved boundaries. The numerical methods are matched using a special algorithm taking into account the features of the transition from unstructured tetrahedral to regular structured meshes in three-dimensional space. A comparative convergence analysis of the combined method and the grid-characteristic method on curvilinear structured meshes is performed depending on the step sizes in spatial directions. The wave field of the velocity magnitude is obtained for a perturbation propagating from the source.