Journal
ADVANCES IN WATER RESOURCES
Volume 114, Issue -, Pages 45-63Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2018.02.003
Keywords
Shallow water equations; Element-based Galerkin methods; Dynamic artificial diffusion; De-aliasing; High-order methods; Unified continuous/discontinuous Galerkin; Large Eddy Simulation
Categories
Funding
- ONR Computational Mathematics program
- AFOSR Computational Mathematics
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The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper. (C) 2018 Elsevier Ltd. All rights reserved.
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