Abstract
This paper presents a Godunov-type numerical formulation that is local, conservative and scalable in both accuracy and resolution. The keystone of the framework is to recast a local multi-resolution discontinuous Galerkin formulation and, combine it with multiwavelets (MWDG) to adaptively determine local resolution level by manipulating multiwavelet coefficients driven by one threshold value set by the user. Recent advances in discontinuous Galerkin modelling of the shallow water equations with topography source term are directly transferred to the MWDG framework. The adaptive MWDG model is tested for simulation of transient and steady shallow flow test cases demonstrating ability to model compound flows with appropriate level resolutions, and with comparable predictive quality as uniform mesh counterpart corresponding to highest resolution available.
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