Tracking fronts in solutions of the shallow‐water equations

Abstract

A front‐tracking algorithm of Chern et al. (1986) is tested on the shallow‐water equations, using the Parrett and Cullen (1984) and Williams and Hori (1970) initial state, consisting of smooth finite amplitude waves depending on one space dimension alone. At high resolution the solution is almost indistinguishable from that obtained with the Glimm algorithm. The latter is known to converge to the true frontal solution, but is 20 times less efficient at the same resolution. The solutions obtained using the front‐tracking algorithm at 8 times coarser resolution are quite acceptable, indicating a very substantial gain in efficiency, which encourages application in realistic ocean models possessing two or three space dimensions.