An improved time marching algorithm for GWC shallow water models

Finite element solutions of the shallow water wave equations have found increasing use by researchers and practitioners in the modeling of oceans and coastal areas. Wave equation models successfully eliminate spurious oscillation modes without resorting to artificial or numerical damping. Typically, wave equation models integrate the continuity equation with a three-time-level scheme centered at k and the momentum equation with a two-time-level scheme centered at k+1/2; nonlinear terms are evaluated explicitly. This allows for a computationally-efficient sequential solution procedure. However in highly nonlinear applications, the algorithm becomes unstable for high Courant numbers. In this work, we examine a predictorcorrector algorithm to improve the stability constraint. Two advantages of the predictor-corrector scheme over the alternative of simultaneous integration of the full nonlinear equations are: 1) they can be easily implemented within the framework of existing codes; and 2) they minimize the size of the matrices that must be stored and inverted. Results from an exhaustive series of one-dimensional experiments show that, depending on the bathymetry, grid resolution, and iteration procedure, we can see over a ten-fold increase in the size of the stable time step. Implementation of the most promising algorithm into the 2D/3D circulation model, Adcirc, is in progress.