An application of the Arnoldi's method to a geophysical fluid dynamics problem

Abstract

A new method to find solutions of large linear systems, based on a projection on the Krylov subspace, is shown to be successful when applied to the linearized barotropic and baroclinc primitive equations. These sets of equations are widely used in the simulation of the dynamics of the atmosphere. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted in order to obtain the solution. The iterative Arnoldi's method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows us to treat the important problem of propagation of linear waves in the atmosphere from a more general point of view. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These kinds of problems leading to large unsymmetrical linear system of order 10000 or more can now be successfully tackled by the Krylov approach. Numerical results of a General Circulation Model, linearized around a nonsymmetrical basic state, are here shown for various numbers of degrees of freedom.