A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge-Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.
翻译:介绍了一个用于单相和双相固态中波波传播的高顺序、精密不连续的Galerkin框架。框架属于嵌入式外向技术,它涉及空间离散,使边界和界面条件能够在曲线嵌入式地球图中以高度精度执行。通过对隐含界定的域和边界的高阶二次曲线规则,实现了高度的准确性,而细胞合并战略则解决了小切细胞的存在问题。框架用于分解以一阶超偏动动脉动配方写成的 Elasto动力学的正方程,并使用了精确的 Riemann 求解器,用以计算具有一般厌异特性的不同材料界面的数值通量。然后,空间分解方程式在使用明确的高序Runge-Kutta算法进行时,在使用明确的高序Rutge-Kutta算法进行推进。若干二维和三维的数值测试,包括动态适应性微微缩度测量,以显示高序精度精度精度和精度方法在包含复合单相和双相基的地球动力学分析中的能力。