SWEMniCS: a software toolbox for modeling coastal ocean circulation, storm surges, inland, and compound flooding - npj Natural Hazards
Summary
The 2D depth-integrated SWE arises as a consequence of significantly larger horizontal wavelength scales than vertical, a hydrostatic pressure distribution in the water column, and application of boundary conditions on the sea floor and surface. The SWE is a hyperbolic system of equations, so it is necessary to utilize techniques that provide numerical stability in order to use continuous finite elements effectively. However, the vast majority of these methods with a few exceptions24,62 use fully explicit time integration schemes that require a CFL constraint in order to preserve stability. The test case in section “Wetting and drying” demonstrates the usage of the α scheme within SWEMniCS for both a conservative and non-conservative form of momentum equations. We note that this modification is exact in the formal setting but practically will reduce the number of occurrences of the computation of the nonlinear function f(H) in the weak form due to the fact that ζ doesn’t require the usage of f(H).