### 2004-05

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