We present a hybrid numerical method for computing the propagation of a diffusing passive pollutant in shallow water. The flow is modeled by the SaintVenant system of shallow water equations and the pollutant propagation is described by a convection-diffusion equation. In this paper, we extend the hybrid finite-volume-particle (FVP) method, which was originally introduced in [CK04, CKP06] for t...

We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and hence inheriting advances from both sides. In particular, the method can be viewed as a Gauss-Seidel approach that requires only independent element-by-element ...

In this paper we consider the discretization the Shallow Water equations by means of Residual Distribution (RD) schemes, and review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related to both the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the ...

The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered in this paper. Some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis. After providing well-posedness arguments for the new models, the authors perform some numerical computations that confirm the role played by the cosine effect in various physical configurations. Ke...

In this paper we consider the discretization the Shallow Water equations by means of Residual Distribution (RD) schemes, and review the conditions allowing the exact preservation of some exact steady solutions. These conditions are shown to be related to both the type of spatial approximation and to the quadrature used to evaluate the cell residual. Numerical examples are shown to validate the ...

We develop and evaluate a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface. The global solutions are represen...

The effect of conservation of integral invariants by finite-element discretization schemes of the shallow-water equations as a model for long-term integrations of atmospheric models is investigated. Two finite-element models are used. The first uses rectangular elements and conserves total energy using an intrinsic method. The second model uses triangular elements and a high-accuracy two-stage ...

We describe a fully explicit residual based construction to discretize the shallow water equations with friction on unstructured grids. The approach is by construction exactly well balanced for al the simple known steady equilibria, and it shows a super-covergent behavior for smooth non-trivial equilibria, as the implicit residual schemes considered in (Ricchiuto, J.Sci.Comp. 48,2011). Moreover...