Boundary Conditions for the Shallow Water Equations solved by Kinetic Schemes

By Marie-Odile Bristeau, Benoit Coussin. 2001

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A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, background): “For a thorough discussion of boundary conditions for SWE and fictitious outer states, we refer to [5, 37].”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, background): “…de processus hydrauliques à surface libre en présence de singularités (http://www-rocq.inria.fr/m3n/CatNat/), by HYKE European programme HPRN-CT-2002-00282 (http://www.hyke.org), by EDF/LNHE (E.A., F.B., M.-O.B., B.P.), and by grant KL 611/6 of the Deutsche Forschungsgemeinschaft (R.K.).”
Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method (2003, methodology): “Here we use a kinetic scheme initiated in [1] and developed in [16] and [3].”
A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics (2013, methodology): “The sufficient conditions imposed at the boundaries, combined with equations obtained from the characteristic theory [37, 47, 62, 63], give the information needed for the calculation of the boundary flux for sub/supercritical inflow/outflow, as well as wall boundary conditions.”