2DH numerical model of nonlinear wave propagation based on a hybrid finite-volume and finite-difference scheme

Abstract

A two-dimensional hybrid (2DH) numerical model suitable for nonlinear wave propagation from deep to shallow waters is developed based on a hybrid finite-volume and finite-difference scheme. To utilize this method conveniently, the selected governing equations are derived again in a conservative form. The fourth-order monotonic upstream-centered scheme for conservation laws–total variation diminishing scheme with a Riemann solver is employed to calculate the numerical flux. The finite-difference scheme is employed to discretize the other spatial derivatives, and the third-order strong stability-preserving (SSP) Runge–Kutta scheme is used for time-stepping. Wave breaking is simulated by locally switching the governing equations to nonlinear shallow-water equations when the Froude number exceeds a certain threshold. A comparison of the numerical results and analytical or experimental data showed that the numerical model performs well in simulating nearshore wave propagation.