A hybrid numerical scheme for extended Boussinesq equations

To efficiently solve the extended Boussinesq equations, a hybrid finite-difference and finite-volume scheme is developed. The one-dimensional governing equations are kept in conservation form. The flux term is discretized using the finite volume method, while the remaining terms are discretized using the finite difference method. A Godunov-type high resolution scheme, in conjunction with the Harten-Lax and van Leer (HLL) Riemann solver and the higher accuracy MUSCL (Monotone Upwind Schemes for Scalar Conservation Laws) method for variable reconstruction, is adopted to compute the interface flux. High order central difference formulas are used to discretize the remaining terms. The third order Runge-Kutta method with total variation diminishing (TVD) property is adopted for time marching. Numerical tests are conducted for model validation, and the computed results agree well with experimental data.