Efficient Numerical Computations of Long-Wave Run-Up and Their Sensitivity to Grid Nesting
Résumé
Computation of long-wave run-up has been of high interest in the fields of ocean sciences and geophysics-particularly for tsunami and river flood modeling. An accurate calculation of run-up and inundation requires the numerical model to account for a sequence of critical processes-each of them posing a different challenge to the numerical solution. This study presents the strategic development of a numerical solution technique for Shallow Water Equations with a focus on accuracy and efficiency for long-wave run-up. The present model is based on an explicit second-order Finite Volume scheme over a staggered grid that efficiently achieves fundamental properties such as well-balance and preservation of shock fronts without the need for computationally expensive solvers. The streamlined code serves as a foundation for the implementation of nested grids. Computations of commonly used long-wave benchmark tests showcase that accurate predictions of local extreme run-up can often be achieved with highly refined yet spatially focused nested grids. Strategic grid nesting can lead to stable and accurate solutions of run-up at locations of interest and reduce the computational load to a fraction of what is usually necessary for a comparable solution over a single grid.
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