In this paper, we analyze the stability of equilibrium manifolds hyperbolic shallow water moment equations. Shallow equations describe flows for complex velocity profiles which vary in vertical direction and models can be seen as extensions standard Equilibrium is an important property balance laws that determines linear solutions vicinity manifolds, it a necessary condition stable numerical so...

We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f -plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete div...

WU, W.; SANCHEZ, A., and ZHANG, M., 2011. An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh. In: Roberts, T.M., Rosati, J.D., and Wang, P. (eds.), Proceedings, Symposium to Honor Dr. Nicholas C. Kraus, Journal of Coastal Research, Special Issue, No. 59, pp. 15-26. West Palm Beach (Florida), ISSN 0749-0208. An implicit finite volume scheme is developed to solve t...

The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration...