#### Central-Upwind Schemes for Weakly Compressible Two-layer Shallow-Water Flows

###### Ponente(s): Sarswati Shah ., Gerardo Hernández Dueñas

###### We introduce an approach for describing two-layer shallow water flows in channels with arbitrary cross sections that exhibits weak compressibility [1, 2]. Unlike the conventional method which leads to a conditionally hyperbolic balance law with non-conservative terms, our proposed model is unconditionally hyperbolic. A thorough explanation of the model's characteristics is provided, encompassing entropy inequalities and stability. Additionally, we present a high-resolution, non-oscillatory semi-discrete central-upwind scheme that builds upon existing methods for hyperbolic balance laws. We will delve into the discussion of model properties such as positivity and equilibrium preservation.Along with the description of the scheme and proofs of these properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.
References
[1] G. Hernandez-Duenas, J. Balbas, “A Central-Upwind Scheme for Two-layer Shallow-water Flows with Friction and Entrainment along Channels”, ESAIM: Mathematical Modelling and Numerical Analysis, 55, pp. 2185–2210, 2021.
[2] A. Chiapolino, R. Saurel “Models and methods for two-layer shallow water flows”, Journal of Computational Physics, 371, pp. 1043-1066, 2018.