Accuracy and Stability Analysis of a Fully Implicit Scheme for the Shallow Water Equations

Abstract

A fully implicit scheme proposed by a group located at the Courant Institute is examined and analyzed for its stability and accuracy. The scheme seems to be easily adaptable to numerical integration in large-scale atmospheric models and could be more efficient than the semi-implicit or the split-explicit algorithms currently used in these models. Linear analysis shows us that the fractional step method, applied in the scheme in order to simplify the calculations, introduces truncation errors that affect the Rossby wave propagation. These errors we unimportant when short time steps are used but they become quite substantial for large steps. This result suggests that the proposed technique may not be as attractive as originally anticipated.