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

  • Authors:

  • Zupeng Jia;Shudao Zhang

  • Affiliations:

  • Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China;Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China and Center of Applied Physics and Technology, Peking University, Beijing 1 ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

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.