Adaptive Grid Conference Edinburgh 96: behrens Abstract

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Atmospheric and ocean modelling with an adaptive finite element solver for the shallow-water equations

J Behrens

Alfred-Wegener-Institut für Polar- und Meeresforschung
Institute for Polar and Marine Research
D-27515 Bremerhaven
jbehrens@awi-bremerhaven.de

Abstract

Numerical modelling of atmospheric or oceanic circulation still represents one of the grand challenges of computational sciences. Conventional methods often use finite difference or spectral methods in order to discretize the evolving stationary problem. These methods however, suffer from several limitations. Finite difference methods are cumbersome when complicated boundary conditions are involved, spectral methods are inflexible with respect to complex geometries and do not allow adaptive mesh refinement.

A new computational method for solving the shallow water equations has been developed. This method combines some of the recent developments of geophysical and computational fluid dynamics, like a semi-Lagrangian advection scheme, an adaptive mesh refinement based on a posteriori error estimation, parallelization on a local memory parallel computer, and iterative solution of the linear system derived from a finite element discretization. Dynamic load balancing has been applied in order to achieve high parallel efficiency.

While adaptive mesh refinement can be viewed as a reduction of the order of computational complexitiy with respect to the number of unknowns preserving accuracy, parallelization acts to reduce the time complexity of the application.

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Last modified Fri Jun 21 19:19:10 GB-Eire 1996 (DBD)