An Improved Geometrically Intrinsic Lagrangian-Eulerian Formulation For 2D Shallow Water Equations For Spatially Discontinuous Topography
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We present an improved Lagrangian--Eulerian scheme based on the novel concept of no flow curves recently introduced in the literature combined with a geometrically intrinsic formulation for 2D shallow water equations designed to handle 2D shallow water equations with spatially discontinuous topography. This work was dictated by the fact that geometrically intrinsic shallow water equations are essentially characterized by non-autonomous fluxes. For concreteness, we develop an effective first-order and high-resolution space-time discretization of the balance laws governing the geometrically intrinsic shallow water equations. We provide a representative set of numerical examples to illustrate the accuracy and robustness of the proposed geometrically intrinsic Lagrangian-Eulerian formulation for several nontrivial spatially discontinuous topographies
