Efficient Pressure Solutions for Circulation Prediction

Two formulations of the rigid-lid wind-driven lake circulation model are presented. The first formulation results in the standard quasi-steady elliptic pressure equation. The second, used in variable topography applications, is a time splitting formulation resulting in a second-order elliptic pressure equation with coefficients that vary at each time step. These pressure equations are discretized by the finite element method and the quickest equation solver identified as a function of the degree of equation nonlinearity, the time variability of the applied surface wind shear, and permissible computational time step. The equation solvers are standard, readily available, easily programmable, and included optimal successive over relaxation, double sweep successive over relaxation, Aitken acceleration, direct Gaussian elimination with back-substitution, and direct Gaussian elimination with repeated elimination. The conclusion was that for large incremented changes in boundary loadings over the numerical time step, direct elimination results in considerable computation savings.