Kezhao Fang

Modelling of 2-D extended Boussinesq equations using a hybrid numerical sc-heme

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen’s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.

Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

ABSTRACT This paper presents a depth-integrated, non-hydrostatic model for coastal water waves. The shock-capturing ability of this model is its most attractive aspect and is essential for computation of energetic breaking waves and wet–dry fronts. The model is solved in a fraction step manner, where the total pressure is decomposed into hydrostatic and non-hydrostatic parts. The hydrostatic pressure component is integrated explicitly in the framework of the finite volume method, whereas most of the existing models use the finite difference method. The fluxes across the cell faces are computed in a Godunov-based manner through an efficient multi-stage scheme. The flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Wave breaking is treated as a shock by locally switching off the non-hydrostatic pressure in the wave front. A moving shoreline boundary is also incorporated. The robustness and accuracy of the developed model are demonstrated through numerical tests.

Fully Nonlinear Modeling Wave Transformation over Fringing Reefs Using Shock-Capturing Boussinesq Model

ABSTRACT Fang, K.Z.; Liu, Z.B., and Zou, Z.L., 2016. Fully nonlinear modeling wave transformation over fringing reefs using shock-capturing Boussinesq model. A numerical model, which solves the horizontal two-dimensional fully nonlinear Boussinesq equations using a well-balanced shock-capturing scheme, is developed and used to investigate wave transformation in a fringing reef environment. The governing equations are first reformulated into a conservative form, and a Godunov-type finite volume method is then used to deal with the convective parts, while the remaining terms are discretized using the finite difference method. Special attention focuses on obtaining a well-balanced state between numerical flux and the source term to model moving wet–dry fronts accurately. The third-order Runge-Kutta scheme with the strong stability preserving property and adaptive time step is used for time marching. After being validated against the analytical solution of exact solitary wave propagation, the proposed model is run to simulate solitary wave transformation over two-dimensional and three-dimensional reefs, and the computed results are in satisfactory agreement with the experimental data.

Boussinesq Modelling of Nearshore Waves Under Body Fitted Coordinate

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates, to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations. The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation. The developed model is used to simulate nearshore wave propagations under curvilinear coordinates, the numerical results are compared against analytical or experimental data with a good agreement.

Reproducing Laboratory-Scale Rip Currents on a Barred Beach by a Boussinesq Wave Model

The pioneering work of Haller [8] on physically investigating bathymetry-controlled rip currents in the laboratory is a standard benchmark test for verifying numerical nearshore circulation models. In this paper, a numerical model based on higher-order Boussinesq equations was developed to reproduce the number of experiments involved in such an investigation, with emphasis on the effect of computational domain size on the numerical results. A set of Boussinesq equations with optimum linear properties and second-order full nonlinearity were solved using a higher-order finite difference scheme. Wave breaking, moving shoreline, bottom friction, and mixing were all treated empirically. The developed model was first run to simulate the rip current under full spatial and time-domain conditions. The computed mean quantities, including wave height, mean water level, and mean current, were compared with the experimental data and favorable agreements were found. The effects of computational domain size on the computation results were then investigated by conducting numerical experiments. The Willmott index was introduced to evaluate the agreements between the computed results and data. Inter-comparisons between the computation results and measurements demonstrated that the computational domain size significantly influenced the numerical results. Thus, running a Boussinesq wave model under full spatial and time-domain conditions is recommended to reproduce Hallers experiment.