Control‐oriented models of the shallow water equations using energy‐conserving discretization schemes
Luca Mayer,
Jens Wurm,
Frank Woittennek
Abstract:In this study, we introduce higher‐order approximation schemes for a 1D shallow‐water model with a moving boundary and arbitrary cross‐section. The model equations are formulated using Lagrange coordinates to handle the time‐varying spatial domain. By discretizing the action functional on a material‐fixed grid and applying an appropriate quadrature scheme, we derive a finite‐dimensional model. This model, taking mass conservation into account as an auxiliary condition, results in a system of semi‐explicit diff… Show more
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