A two-grid finite difference method for the primitive equations of the ocean

A two-level method is proposed for the finite difference approximation of a class of dissipative systems including the primitive equations of the ocean. The two-level (or multilevel) method amounts to solving a nonlinear problem on the single coarsest grid; subsequent approximations are generated on a succession of refined meshes by solving a linearized problem about the solution on the previous level. The stability analysis for an Euler-type scheme shows that the multilevel method can allow larger time steps than the traditional one-level methods. Some numerical simulations of the primitive equations of the ocean using this new multi-scale algorithm are presented to illustrate the method.