A Lagrangian cell-centered discontinuous Galerkin hydrodynamic method for 2D Cartesian and RZ axisymmetric coordinates

摘要

We present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the gas dynamic equations on unstructured hybrid meshes in 2D Cartesian and RZ axisymmetric coordinates. For 2D RZ axisymmetric coordinates, the method is based on a true volume scheme. The physical conservation laws for the mass, momentum and total energy are discretized using the DG approach. The specific volume, velocity and specific total energy are approximated with linear Taylor expansions on a reference element.The nodal velocity, and the corresponding forces, are calculated by solving a multidirectional approximate Riemann problem at the element nodes. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy in 2D Cartesian and RZ axisymmetric coordinates. A suite of test problems are presented to demonstrate the robustness and expected second order accuracy of this new method.