An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations

We present a high-order well-balanced unstructured finite volume (FV) scheme on triangular meshes for modeling weakly nonlinear and weakly dispersive water waves over slowly varying bathymetries, as described by the 2D depth-integrated extended Boussinesq equations of Nwogu, rewritten here in conservation law form. The FV scheme numerically solves the conservative form of the equations following the median dual node-centered approach, for both the advective and dispersive part of the equations. For the advective fluxes, the scheme utilizes an approximate Riemann solver along with a well-balanced topography source term upwinding. Higher order accuracy in space and time is achieved through a MUSCL-type reconstruction technique and through a strong stability preserving explicit Runge–Kutta time stepping. Special attention is given to the accurate numerical treatment of moving wet/dry fronts and boundary conditions. The model is applied to several examples of non-breaking wave propagation over variable topographies and the computed solutions are compared to experimental data. The presented results indicate that the presented FV model is robust and capable of simulating wave transformations from relatively deep to shallow water, providing accurate predictions of the wave's propagation, shoaling and runup.

► A novel approach for numerically integrating Nwogu's 2D Boussinsesq equations on unstructured meshes.
► Equations recast in conservation law form, having an identical flux term as the nonlinear shallow water equations.
► A higher-order well-balanced finite volume scheme is developed with accurate treatment for shoreline motion.
► The approach combines state of the art discretizations and accurately simulates wave shoaling and runup.