Runge-Kutta control volume (RKCV) discontinuous finite element method for multi-medium fluid simulations is constructed. Linear and nonlinear Riemann solvers are used for numerical flux at fluid interfaces. The method preserves local conservation and high-resolution. Numerical results show that even with a linear Riemann solver the schemes works well. Comparisons with Runge-Kutta discontinuous Galerkin method show advantages of RKCV method.

We present a Lagrangian scheme for one-dimensional Euler equations.The scheme uses Runge-Kutta discontinuous Galerkin (RKDG) finite element method to solve Euler equations under Lagrangian framework.The mesh moves with fluid flow.The scheme is conservative for density,momentum and total energy.It achieves second-order accuracy both in space and time.Numerical tests are presented to demonstrate accuracy and non-oscillatory properties of the scheme.

We present a Lax-Wendroff discontinuous Galerkin (LWDG) method combining with adaptive mesh refinement (AMR) to solve three-dimensional hyperbolic conservation laws. Compared with Runge-Kutta discontinuous finite element method (RKDG) the method has higher efficiency. We give an effective adaptive strategie. Equidistribution strategy is easily implemented on nonconforming tetrahedral mesh. Error indicator is introduced to solve three-dimensional Euler equations. Numerical experiments demonstrate that the method has satisfied numerical efficiency.