Performance of iterative algorithms for the solution of the shallow-water equations

We discuss the performance of iterative solution methods implemented in a 3D model of the shallow water equations used to simulate the propagation of tidal waves in stratified ocean domains. The model uses a harmonic approach by means of which the transient problem is transformed into a number of steady-state nonlinear problems (one per each tidal frequency considered). For the vertical interpolation of the model variables, a spectral decomposition in terms of an orthogonal set of basis functions is applied. A Picard iteration is used to solve the nonlinear systems of equations, and a preconditioned conjugate gradient method is used to solve the intermediate linear systems. We report 3D numerical results of the tidal circulation in the Strait of Gibraltar, and we compare the performance of different conjugate gradient methods implemented in the model with the performance obtained with classical direct methods.