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TVD adaptive mesh redistribution scheme for the shallow‐water equations

This work presents a high‐resolution scheme combined with a moving mesh method for approximating the solution of shallow water system. The main difficulties in deriving stable and convergent numerical approximations can be due to solutions that vanish in nontrivial parts of domain such as dry states in water flows. In these situations, the coupling between characteristic fields gradually increases as water height is stepped down. The basic methodology in our method is to avoid characteristic decompositions in the spatial discretization. Moving dry regions within the computing domain are captured without the appearance of negative values. The high‐resolution properties of the scheme as well as its resistance to mesh orientation gives the great potential of the moving mesh methods for reducing computational costs without sacrificing the overall level of accuracy, which is demonstrated in a variety of hydraulic examples. Copyright © 2007 John Wiley & Sons, Ltd.