A conservative adaptive wavelet method for the shallow-water equations on the sphere

Adaptive wavelet collocation method on the shallow water model

Article history: Received 20 May 2013 Received in revised form 10 March 2014 Accepted 25 March 2014 Available online 1 April 2014

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 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...

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