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2004-05

A Runge-Kutta Discontinuos Galerkin Method for the Euler Equations

by Tang, H., Warnecke, G..


Series: 2004-05, Preprints

MSC:
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

This paper was published in:
Computers & Fluids