학술논문
A well-balanced, positive, entropy-stable, and multi-dimensional-aware finite volume scheme for 2D shallow-water equations with unstructured grids.
Document Type
Journal
Author
Del Grosso, Alessia (F-UBORD-IM) AMS Author Profile; Castro, Manuel J. (E-MAL-MA) AMS Author Profile; Chan, Agnes (F-UBORD-IM) AMS Author Profile; Gallice, Gérard (F-UBORD-IM) AMS Author Profile; Loubère, Raphaël (F-CEAL9) AMS Author Profile; Maire, Pierre-Henri AMS Author Profile
Source
Subject
65 Numerical analysis -- 65M Partial differential equations, initial value and time-dependent initial-boundary value problems
65M08Finite volume methods
76Fluid mechanics -- 76B Incompressible inviscid fluids
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65M08
76
76B15
Language
English
ISSN
10902716
Abstract
Summary: ``In this article, we present a multi-dimensional-awareEulerian Riemann Solver (RS) and its associated Finite Volume (FV)scheme for the 2D Shallow-Water (SW) equations. This RS, appropriatelyderived from its associated Lagrangian version, presents the specificfeature of coupling all cells in the vicinity of the current one.Consequently, this solver is no longer a 1D RS across one edge.Contrarily, it encounters for genuine multidimensional effects and forthe presence of the source term of the SW equations. The associatedfirst order FV numerical scheme ensures well-balancing for lake at reststeady states, positivity preservation and entropy stabilityproperties. Moreover, a second-order accurate extension is proposedbased on RungeKutta time discretization and piecewise linear limitedreconstructions, that preserve the wellbalanced character of the firstorder scheme. We present several 2D tests assessing the good behaviorsof the obtained numerical scheme on unstructured mesh. The numericalscheme seems insensitive to spurious numerical instabilities such asthe carbuncle effect.''