A look back at 20 years of GWC-based shallow water models

Wave continuity equation models were introduced in 1979 by Lynch and Gray as a means to suppress spurious oscillations that appeared in finite element models based on the primitive equations. Since then, the basic algorithm has been studied and tested extensively; with subsequent modifications and extensions, it has proven to be a computationally efficient, reliable algorithm for predicting the hydrodynamic behavior of coastal and oceanic waters. Modifications over the last 20 years can be broken into two broad, but inter-related classes: 1) changes to the numerical algorithm, e.g., implicit time-marching or higher order elements; 2) incorporating more of the underlying physics into the mathematical formulation, e.g., baroclinic forcing or wetting and drying of near-shore elements. This manuscript summarizes the algorithm’s evolution and highlights some its strengths as well as its shortcomings. It closes with some observations about the future of shallow water algorithms based on the generalized wave continuity (GWC) equation.