A semi-implicit fully exactly well-balanced relaxation scheme for the shallow water system. - Caballero Cárdenas, Celia; Castro-Díaz, Manuel Jesús; Chalons, Christophe; Morales-de-Luna, Tomás; Muñoz-Ruiz, María de la Luz (SIAM, 2024)
This article focuses on the design of semi-implicit schemes that are fully well-balanced for the one-dimensional shallow water equations, that is, schemes that preserve all smooth steady states of the system and not just water-at-rest equilibria. The proposed methods outperform standard explicit schemes in the low-Froude regime, where the celerity is much larger than the fluid velocity, eliminating the need for a large number of iterations on large time intervals. In this work, splitting and relaxation techniques are combined in order to obtain fully well-balanced semi-implicit first and second order schemes. In contrast to recent Lagrangian-based approaches, this one allows the preservation of all the steady states while avoiding the complexities associated with Lagrangian formalism.
Artículo en open access
Keywords: Análisis numérico; Magnetohidrodinámica; fully exactly well-balanced schemes; Relaxation schemes; Semi-implicit schemes; Shallow water