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math.NA2023
Active flux for triangular meshes for compressible flows problems
Rémi Abgrall, Jianfang Lin, Yongle Liu
In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and th…
math.NA2023
A New Approach for Designing Well-Balanced Schemes for the Shallow Water Equations: A Combination of Conservative and Primitive Formulations
Remi Abgrall, Yongle Liu
In this paper, we introduce a new approach for constructing robust well-balanced numerical methods for the one-dimensional Saint-Venant system with and without the Manning friction…