A limitation of some well-balanced schemes for Shallow Water equations
Résumé
Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. They allow to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid the unstabilities when dealing with dry zones. In this note, we prove that the well-balanced scheme based on hydrostatic reconstruction proposed in 2004 [2] exhibits an abnormal behavior for some combinations of slope, mesh size and water height.
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