Dispersive Shallow Water Wave Modelling. Part IV: Numerical Simulation on a Globally Spherical Geometry

摘要

In the present manuscript, we consider the problem of dispersive wavesimulation on a rotating globally spherical geometry. In this Part IV, we focuson numerical aspects while the model derivation was described in Part III. Thealgorithm we propose is based on the splitting approach. Namely, equations aredecomposed on a uniformly elliptic equation for the dispersive pressurecomponent and a hyperbolic part of shallow water equations (on a sphere) withsource terms. This algorithm is implemented as a two-step predictor-correctorscheme. On every step, we solve separately elliptic and hyperbolic problems.Then, the performance of this algorithm is illustrated on model idealisedsituations with an even bottom, where we estimate the influence of sphericityand rotation effects on dispersive wave propagation. The dispersive effects arequantified depending on the propagation distance over the sphere and on thelinear extent of generation region. Finally, the numerical method is applied toa couple of real-world events. Namely, we undertake simulations of theBulgarian 2007 and Chilean 2010 tsunamis. Whenever the data is available, ourcomputational results are confronted with real measurements.