Space–time SUPG formulation of the shallow‐water equations

We present a new space–time SUPG formulation of the shallow‐water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock‐capturing parameter. In the context of two test problems, we evaluate the performance of the new shock‐capturing parameter. We also evaluate the performance of the space–time SUPG formulation compared to the semi‐discrete SUPG formulation, where the system of semi‐discrete equations is solved with the central‐difference (Crank–Nicolson) time‐integration algorithm. Copyright © 2010 John Wiley & Sons, Ltd.