Runge-Kutta discontinuous Galerkin methods for compressible two-medium flow simulations: One-dimensional case

  • Authors:

  • Jianxian Qiu;Tiegang Liu;Boo Cheong Khoo

  • Affiliations:

  • Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing, Jiangsu 210093, PR China and Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singa ...;Institute of High Performance Computing, 01-01 The Capricorn, Singapore Science Park II, Singapore 117528, Singapore;Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore and Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 1 ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

The Runge-Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge-Kutta time discretizations, and limiters. In this paper, we investigate using the RKDG finite element method for compressible two-medium flow simulation with conservative treatment of the moving material interfaces. Numerical results for both gas-gas and gas-water flows in one-dimension are provided to demonstrate the characteristic behavior of this approach.