A Fully Implicit Scheme for the Barotropic Primitive Equations

S. E. Cohn Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
Department of Mathematics, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro-RJ, CEP 22453, Brazil

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D. Dee Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
Department of Mathematics, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro-RJ, CEP 22453, Brazil

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D. Marchesin Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
Department of Mathematics, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro-RJ, CEP 22453, Brazil

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E. Isaacson Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012

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G. Zwas Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
Division of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel

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Abstract

An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires at each time step the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Our experience indicates that this implicit method is practical for numerical simulation on fine meshes.

Abstract

An efficient implicit finite-difference method is developed and tested for a global barotropic model. The scheme requires at each time step the solution of only one-dimensional block-tridiagonal linear systems. This additional computation is offset by the use of a time step chosen independently of the mesh spacing. The method is second-order accurate in time and fourth-order accurate in space. Our experience indicates that this implicit method is practical for numerical simulation on fine meshes.

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