Fourth order finite volume solution to shallow water equations and applications

This study presents the fourth order accurate finite volume solution to shallow water equations. Fourth order accuracy in space was provided by using the Monotone Upstream‐centered Schemes for Conservation Laws–Total Variation Diminishing scheme, whereas fourth order accurate solution in time was achieved by using the third order predictor scheme of Adams–Basforth followed by the fourth order corrector scheme of Adams–Moulton. The applicability and accuracy of the solution algorithm were explored on complex flow conditions. These flow conditions cover a theoretical well‐known partial two‐dimensional dam break problems and an experimental flow in a compound channel with or without a bridge. The applicability limits of the solution algorithm were discussed. The overall performance of the solution was found to be reasonably good. Copyright © 2013 John Wiley & Sons, Ltd.