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

By Fengyan Shi, James T. Kirby, Jeffrey C. Harris, Joseph D. Geiman, Stephan T. Grilli. 2012

638 citations recorded by the source corpus.

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 waveaveraged nearshore circulation.

Subfields: Atmospheric Science, Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/cf6337c3843442d68fe4665d046c4b73de7867d2

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Citations in the corpus

Dispersion of tsunamis: does it really matter? (2013, methodology): “A potential massive volcanic flank collapse at La Palma Island was first suggested by Ward (2001). Assuming a slide volume of 500 km3, they predicted wave heights along the east coast of North America in the range 10–25 m.”
A new approach to handle wave breaking in fully non-linear Boussinesq models (2012, methodology): “, 2003), but also recently within the framework of fully-non‐linear BT models (Shi et al., 2012).”
Numerical modeling of tsunami waves generated by the flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands): Tsunami source and near field effects (2012, methodology): “…away from La Palma, to organize as a radially propagating wave train, with a few leading longer waves, THETIS’ ouputs are used to initialize a fully nonlinear and dispersive Boussinesq long wave model (FUNWAVE-TVD) [Shi et al., 2012], which is then used to further propagate the tsunami (Figure 1b).”
Dispersive tsunami waves in the ocean: Model equations and sensitivity to dispersion and Coriolis effects (2013, methodology): “…nonlinear wave evolution in shallow coastal margins as well as mainly linear evolution in the deep ocean basin, we will retain the mechanics of the fully nonlinear Boussinesq model framework, following the approach of Chen (2006) and Shi et al. (2012a) but working in the framework of rotating flow.”
A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations (2015, methodology): “While [4] proposed to do this using Strang splitting, we note that adding arbitrary source terms to the Saint-Venant system (or other systems of time-dependent partial differential equations) can often be done simply by including this source term in the appropriate stages of the time integration sch”
Numerical simulation of tsunami waves generated by deformable submarine landslides (2013, methodology): “, 1983) is used to estimate fluxes at the cell faces, which has widely been proved to be robust and efficient (Shi et al., 2012; Ma et al., 2012).”
Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations (2013, methodology): “Thus, three types of initializations are tested and compared in the regional grid: either (a) a hot start of FUNWAVE-TVD, by specifying the maximum seafloor vertical displacement of each coseismic source (e.g., such as in Fig.”