Modelling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

TL;DR

This paper introduces a high-order accurate implicit-mesh discontinuous Galerkin method for simulating wave propagation in complex elastic solids, effectively handling curved geometries and material interfaces with high precision.

Contribution

The paper presents a novel high-order spatial discretization framework that enforces boundary and interface conditions accurately on curved embedded geometries in elastodynamics simulations.

Findings

Achieves high-order accuracy in wave propagation simulations.

Effectively handles complex geometries and material interfaces.

Demonstrates robustness with adaptive mesh refinement.

Abstract

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.