CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM

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Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods (2008, positive): “In [36] Kurganov and Levy extend HLL scheme with state reconstruction for Shallow Water equation with topography as source term, using the water surface and the discharge as unknowns.”
Well‐balanced positivity preserving central‐upwind scheme for the shallow water system with friction terms (2015, methodology): “x; t/ dx, which are evolved in time according to the semi-discrete central-upwind scheme [8, 9, 27]:”
Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations (2004, methodology): “The central WENO schemes for the hyperbolic conservation laws were developed by Levy et al. [20].”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Another popular approach is to rewrite the equation in terms of the water surface instead of water height (also referred as the pre-balanced formulation), and well-balanced methods [31, 48, 69] can be designed based on such formulation.”
Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws (2003, methodology): “Previous schemes have also been modified for this target by Bermudez and Vasquez [1] and some different approaches are developed in [22],[23] and [18].”