A General Procedure To Construct High-Order Well-Balance Finite Volume Schemes For 1D Hyperbolic Balance Laws With Singular Source Terms
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In this talk we will show a general framework to construct explicit, explicit-implicit or fully implicit well-balanced finite volume schemes for balance laws with singular source terms. The proposed framework relies on the combination of the Generalized Hydrostatic Reconstruction technique (GHR, see Castro-Pardo-Pares 2007) and a well-balanced reconstruction operator following the ideas described in Castro-Pares 2020. First these two ingredients are recalled as well as the family of semi-discrete in space well-balanced high-order methods obtained by applying them. Then, time discretization is discusses with special emphasis on the explicit-implicit and fully implicit discretizations. In particular, two new strategies to design well-balanced implicit finite volume schemes for systems with singular source terms will be presented. Finally, the performance of the proposed methods with shown with some numerical tests
