A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions

作者：Jia Zupeng; Zhang Shudao^*

来源：Journal of Computational Physics, 2011, 230(7): 2496-2522.

DOI：10.1016/j.jcp.2010.12.023

• Cell-centered Lagrangian scheme
• High-order schemes
• Runge-Kutta discontinuous Galerkin method
• Geometrical conservation law
• HWENO reconstruction
• Compressible Euler equations

This paper presents a new high-order cell-centered Lagrangian scheme for two-dimensional compressible flow. The scheme uses a fully Lagrangian form of the gas dynamics equations, which is a weakly hyperbolic system of conservation laws. The system of equations is discretized in the Lagrangian space by discontinuous Galerkin method using a spectral basis. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently in the Eulerian space by virtue of an improved nodal solver. The nodal solver uses the HLLC approximate Riemann solver to compute the velocities of the vertex. The time marching is implemented by a class of TVD Runge-Kutta type methods. A new HWENO (Hermite WENO) reconstruction algorithm is developed and used as limiters for RKDG methods to maintain compactness of RKDG methods. The scheme is conservative for the mass, momentum and total energy. It can maintain high-order accuracy both in space and time, obey the geometrical conservation law, and achieve at least second order accuracy on quadrilateral meshes. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.

• 出版日期2011-4-1
• 单位北京应用物理与计算数学研究所; 北京大学