Application of Nodal Discontinuous Galerkin Finite Element Method for 2d Nonlinear Elastic Wave Propagation

In order to solve the elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured meshes, a nodal Discontinuous Galerkin Finite Element Method (DG-FEM) is presented, which combines the geometrical flexibility of the Finite Element Method and strongly nonlinear wave simulation capability of the Finite Volume Method. The equations of nonlinear elastodynamics have been written in a conservative form in order to facilitate the numerical implementation and introduce different kinds of elastic nonlinearities, such as the classical nonlinearities and non-classical hysteretic nonlinearities. In the calculation of DG-FEM scheme, different kinds of boundary conditions and numerical fluxes have been discussed. The numerical simulations of linear elastic wave propagation and plane wave nonlinear propagation demonstrated the developed DG-FEM scheme has an excellent precision and performance in numerical application.