A Runge-Kutta Discontinuos Galerkin Method for the Euler Equations
Preprint series: 04-05, Preprints
The paper is published: Computers & Fluids
- 35L65 Conservation laws
- 65M06 Finite difference methods
- 65M99 None of the above but in this section
Abstract: This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for the Euler equations of gas dynamics from the viewpoint of kinetic theory. Like the traditional gas-kinetic schemes, our RKDG method will not need the characteristic decompostion as well as the exact or approximate Riemann solver in computing the numerical flux at the surface of the finite elements; the integral term containing the nonlinear flux can be exactly calculated at the microscopic level. To suppress numerical oscillation, a limiting procedure is also designed carefully. Some numerical experiments are conducted. The results show that a higher-order accurate rate of convergence can be obtained by using our RKDG methods to solve a smooth problem; shock waves and contact discontinuous can be well-captured.
Keywords: Runge-Kutta discontinuous Galerkin method, the Euler equations the Boltzmann equation, high order accuracy
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