Testing finite differencing schemes for the shallow water equations

Abstract

The explicit, the semi-implicit, and the fractional step schemes are tested and compared in the

solution of the shallow water equations. The explicit finite-difference formulation is the most accurate, but is restricted by a stability condition which is not suitable for long-term numerical simulations. The standard semi-implicit scheme requires the solution of an elliptic equation which is also timeconsuming.

The fractional step method results in the least accurate, but computationally the most efficient solution.