ROBUST MULTIGRID SOLUTION OF THE SHALLOW-WATER BALANCE-EQUATIONS

Balance Equation models describing accurate, gravity-wave-free states on the so-called ''slow manifold'' of the Primitive Equations are of w ide and growing interest, both theoretical and practical, for geophysi cal fluid dynamics. As a particular example with only two spatial dime nsions, the Shallow-Water Balance Equations are a coupled, highly nonl inear, nonsymmetric system of partial differential equations, for whic h only ad hoc solvers of limited robustness have previously been devel oped. Two multigrid algorithms are presented, one explicit and one imp licit in time, which are shown by analysis and numerical examples to b e efficient and robust solution techniques for this system. These exam ples include modons and Shallow-Water turbulence at finite Rossby numb er, It is found that, in some regimes of physical parameters, quite la rge time steps can be taken with the implicit solver, with little loss of accuracy or efficiency. This is interpreted as due to significantl y slower evolutionary rates of the dominant patterns compared to parce l trajectory rates. (C) 1995 Academic Press. Inc.