An Adaptive Mesh Refinement Solver for Regularized Shallow Water Equations

Introduction. We present a novel adaptive mesh refinement (AMR) solver, SWqgdAMR, based on the open software platform AMReX. The new solver is grounded in regularized shallow water equations. This paper details the equations, their discretization, and implementation features within AMReX. The efficacy of SWqgdAMR is demonstrated through two test cases: a two-dimensional circular dam break (collapse of a liquid column) and the collapse of two liquid columns of different heights.
Materials and Methods. The SWqgdAMR solver is developed to extend the applicability of regularized equations in problems requiring high computational power and adaptive grids. SWqgdAMR is the first solver based on the quasigas dynamic (QGD) algorithm within the AMReX framework. The implementation and validation of SWqgdAMR represent a crucial step towards the further expansion of the QGD software suite.
Results. The AMReX-based shallow water equations solver SWqgdAMR with adaptive mesh refinement is described and tested in detail. Validation of SWqgdAMR involved two-dimensional problems: the breach of a cylindrical dam and the breach of two cylindrical dams of different heights. The presented solver demonstrated high efficiency, with the use of adaptive mesh refinement technology accelerating the computation by 56 times compared to a stationary grid calculation.
Discussion and Conclusions. The algorithm can be expanded to include bathymetry, external forces (wind force, bottom friction, Coriolis forces), and the mobility of the shoreline during wetting and drying phases, as has been done in individual codes for regularized shallow water equations (RSWE). The current implementation of the QGD algorithm did not test the potential for parallel computing on graphical cores.

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