The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and...The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.展开更多
文摘The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.
