A Linear ADI Method for the ShallowWater Equations
Abstract
A new ADI method is proposed for the approximate solution of the shallowwater equations. Based on a perturbation of a linearized CrankNicolsontype discretization, this method is algebraically linear and also locally secondorder correct in time. Its performance on a test problem given in [1] demonstrates that it requires less computer time per time step than the fastest quasiNewton method proposed in [1], and for given mesh parameters it appears to be marginally more accurate. The results of several long runs are also reported, and phenomena similar to those described in [14] are exhibited. In particular, it is shown that neither the new method nor the best of the methods of [1] conserves potential enstrophy and, as a result, after a finite time, these methods always "blow up."
 Publication:

Journal of Computational Physics
 Pub Date:
 August 1980
 DOI:
 10.1016/00219991(80)900017
 Bibcode:
 1980JCoPh..37....1F
 Keywords:

 Alternating Direction Implicit Methods;
 Boundary Value Problems;
 Finite Difference Theory;
 Flow Equations;
 Run Time (Computers);
 Shallow Water;
 Water Flow;
 Linearization;
 Newton Methods;
 Nonlinear Equations;
 Partial Differential Equations;
 Perturbation Theory;
 Fluid Mechanics and Heat Transfer