THE LATTICE STRUCTURE OF THE FINITE-DIFFERENCE PRIMITIVE AND VORTICITY EQUATIONS

GEORGE W. PLATZMAN The University of Chicago, Chicago, Ill.

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Abstract

The use of central differences on a rectangular net, in solving the primitive or vorticity equations, produces solutions on each of two lattices. By exploring this lattice structure, a formal equivalence is established between the central-difference vorticity and primitive equations. A demonstration is given also that exponential instability previously found to result from certain types of boundary conditions is suppressed by applying these conditions in such a way as to avoid coupling the lattices.

Abstract

The use of central differences on a rectangular net, in solving the primitive or vorticity equations, produces solutions on each of two lattices. By exploring this lattice structure, a formal equivalence is established between the central-difference vorticity and primitive equations. A demonstration is given also that exponential instability previously found to result from certain types of boundary conditions is suppressed by applying these conditions in such a way as to avoid coupling the lattices.

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