Dispersive Shallow Water Wave Modelling. Part IV: Numerical Simulation on a Globally Spherical Geometry (Communications in Computational Physics, 2018)
In the present manuscript we consider the problem of dispersive wave simulationon a rotating globally spherical geometry. In this Part IV we focus on numericalaspects while the model derivation was described in Part III. The algorithm wepropose is based on the splitting approach. Namely, equations are decomposed on auniform elliptic equation for the dispersive pressure component and a hyperbolic partof shallow water equations (on a sphere) with source terms. This algorithm is implementedas a two-step predictor-corrector scheme. On every step we solve separatelyelliptic and hyperbolic problems. Then, the performance of this algorithm is illustratedon model idealized situations with even bottom, where we estimate the influence ofsphericity and rotation effects on dispersive wave propagation. The dispersive effectsare quantified depending on the propagation distance over the sphere and on the linearextent of generation region. Finally, the numerical method is applied to a coupleof real-world events. Namely, we undertake simulations of the BULGARIAN 2007 andCHILEAN 2010 tsunamis. Whenever the data is available, our computational resultsare confronted with real measurements.
Keywords: Finite volumes; splitting method; nonlinear dispersive waves; spherical geometry; rotating sphere; Coriolis force.