Sesión Análisis Numérico y OptimizaciónOn the robustness and fully discrete entropy stability of three-point well-balanced finite-volume schemes
Manuel Jesús Castro Díaz
Universidad de Málaga. Dpto. Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
This presentation introduces a simple and robust approach to enforce discrete entropy stability in first-order well-balanced finite volume schemes for systems of balance laws, including those with non-conservative terms. Building on Tadmor’s artificial viscosity method and its recent extensions, the authors present an entropy-preserving modification that can be applied to a broad class of three-point schemes. The key contribution is the design of a viscosity coefficient that preserves the well-balanced property while ensuring entropy dissipation at the discrete level. A rigorous theoretical framework is established to guarantee robustness, well-balancing, and entropy stability under an appropriate CFL condition. The effectiveness of the method is demonstrated through numerical experiments on shallow water systems and two-layer flows, confirming both accuracy and stability
Trabajo en conjunto con: Christophe Berthon (Université de Nantes, Laboratoire de Mathématiques Jean Leray. Francia), Ludovic Martaud (Université Rennes, Inria Rennes and IRMAR UMR CNRS 6625, F-35042 Rennes, Francia) y Tomás Morales de Luna (Universidad de Málaga, Dpto Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada. España).
Referencias
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