High-resolution Relaxed Scheme for Dam-break Problems

Numerical models are an important tool to simulate dam-break flows. A high-resolution relaxed scheme is proposed for simulating one-dimensional dam-break problems. The scheme is based on combining relaxation approximation with an improved fifth-order weighted essentially nonoscillatory (WENO) reconstruction and third-order strong stability preserving (SSP) Runge-Kutta scheme. The new method enjoy the main advantage of the relaxation schemes, namely it avoid Riemann solvers, characteristic decomposition and the computation of Jacobians. The numerical experiments demonstrate the efficiency of our method.