STABILITY ANALYSIS OF AN ODD-EVEN-LINE HOPSCOTCH METHOD FOR 3-DIMENSIONAL ADVECTION-DIFFUSION PROBLEMS

A linear stability analysis is given for an odd-even-line hopscotch (O ELH) method, which has been developed for integrating three-space dime nsional, shallow water transport problems. Sufficient and necessary co nditions are derived FOE strict von Neumann stability for the case of the general, constant coefficient, linear advection-diffusion model pr oblem. The analysis is based on an equivalence with an associated sche me which is composed of the Leapfrog, the Du Fort-Frankel, and the Cra nk-Nicolson schemes. The results appear to be rather intricate. For ex ample, the resulting expressions for critical stepsizes reveal that th e presence of horizontal diffusion generally leads to a smaller value, in spite of the fact that we have unconditional stability for pure di ffusion problems. It is pointed out that this is due to the Du Fort-Fr ankel deficiency. On the other hand, it is also shown, by a numerical experiment, that in practice it is sufficient to obey the weaker Coura nt-Friedrichs-Lewy (CFL) condition associated with the case of pure ho rizontal advection, unless a huge number of integration steps are to b e taken.