Hybrid finite volume – finite difference scheme for 2DH improved Boussinesq equations

In this paper, a hybrid scheme based on a set of 2DH extended Boussinesq equations for slowly varying bathymetries is introduced. The numerical code combines the finite volume technique, applied to solve the advective part of the equations, with the finite difference method, used to discretize dispersive and source terms. Time integration is performed using the fourth-order Adams–Bashforth–Moulton predictor–corrector method; the Riemann problem is solved employing an approximate HLL solver, a fourth-order MUSCL-TVD technique is applied. Five test cases, for non-breaking and breaking waves, are reproduced to verify the model comparing its results to laboratory data or analytical solutions.