Pseudo-spectral/finite-difference adaptive method for spherical shallow-water equations

Abstract

The shallow-water equations (SWEs) describing a thin layer of fluid flow (liquid or gas) in two dimensions are the simplest possible model capturing the essential characteristics of fluid flow on a sphere. In this paper we present a p-adaptive method based on higher-order finite differences and pseudo-spectral derivatives which is used to solve SWEs on a sphere. The numerical experiments confirm the expected high-order accuracy.

Keywords:

• Shallow-water equations
• p-adaptive equations
• Finite-difference equations
• Pseudo-spectral equations
• Partial differential equations

Acknowledgements

The authors acknowledge support from Ministerio de Educación y Ciencia, Spain (Project CGL2004–04095/CLI) and Consejería de Educación y Ciencia de la Junta de Comunidades de Castilla-la Mancha, Spain (Project PA106–0123–7821).