 |
This paper presents a new one-dimensional (1D) third-order Runge–Kutta discontinuous Galerkin (RKDG3) scheme for shallow flow. The shallow water equations that adopt water level as a flow variable are solved by an RKDG3 scheme to give piecewise linear approximate solutions, which are locally defined by an average coefficient and a slope coefficient. Extra numerical enhancements are proposed to amend the local coefficients associated with water level in order to maintain the well-balanced property of the RKDG3 scheme for real applications. Friction source terms are included and evaluated using splitting implicit discretization, implemented with a physical stopping condition to ensure stability. steady and unsteady benchmark tests with/without friction effects are considered to demonstrate the performance of the present model.
