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The numerical solution of a system of diffusion/convection equations describing coastal circulation

University of British Columbia

A mathematical model describing nearshore ocean currents is examined. The motivation for the problem is discussed and a derivation of the model equations presented. The model equations consist of a pair of coupled, nonlinear, parabolic partial differential equations. A numerical method, the Crank-Nicolson finite difference scheme, is presented for solving the corresponding linear equations, and the convergence and stability of the method discussed. Methods for dealing with the nonlinear terms, and their effects on accuracy and stability, are examined. The initial and boundary conditions of the model equations present special problems, and we describe methods to solve them. A more efficient finite difference scheme for our equations, based on the Crank-Nicolson formula, is introduced, and its advantages discussed. A computer program incorporating these methods is developed to solve the model equations, and results for test data presented. We conclude with recommendations for additions to the program to model the currents more accurately.

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2010-04-21

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http://hdl.handle.net/2429/23990

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University of British Columbia

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