Efficient solvers for the shallow water equations on a sphere

A Radial Basis Function Method for the Shallow Water Equations on a Sphere

The paper derives the first known numerical shallow water model on the sphere using radial basis function (RBF) spatial discretisation, a novel numerical methodology that does not require any grid or mesh. In order to perform a study with regard to its spatial and temporal errors, two nonlinear test cases with known analytical solutions are considered. The first is global steady-state flow with...

A finite element method for solving the shallow water equations on the sphere

Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each e...

A Hybrid Meshless/Spectral-Element Method for the Shallow Water Equations on the Sphere

1 Introduction and Motivations

A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere

Popular approaches for solving the shallow water equations (SWE) for climate modeling are explicit and semi-implicit methods, both have certain constraints on the time step size. In this paper, we propose and study a fully implicit method which imposes no limit on the time step size, but requires the solution of a large sparse nonlinear system of equations at every time step. The focus of the p...

High Order Cartesian Method for the Shallow Water Equations on a Sphere