A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation

We present a high-order adaptive time-stepping TVD solver for the fully nonlinear Boussinesq model of Chen (2006), extended to include moving reference level as in Kennedy et al. (2001). The equations are reorganized in order to facilitate high-order Runge–Kutta time-stepping and a TVD type scheme with a Riemann solver. Wave breaking is modeled by locally switching to the nonlinear shallow water equations when the Froude number exceeds a certain threshold. The moving shoreline boundary condition is implemented using the wetting–drying algorithm with the adjusted wave speed of the Riemann solver. The code is parallelized using the Message Passing Interface (MPI) with non-blocking communication. Model validations show good performance in modeling wave shoaling, breaking, wave runup and wave-averaged nearshore circulation.

► A Boussinesq model is developed using an adaptive time-stepping TVD solver.
► Adaptive time stepping is efficient in modeling flows with large Froude numbers.
► The TVD scheme is robust in the treatment of wave breaking.
► Wetting–drying method is better than the slot method in modeling moving shoreline.