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
Abstract
Summary: ``In this article, we present a multi-dimensional-aware Eulerian Riemann Solver (RS) and its associated Finite Volume (FV) scheme for the 2D Shallow-Water (SW) equations. This RS, appropriately derived from its associated Lagrangian version, presents the specific feature 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 for the presence of the source term of the SW equations. The associated first order FV numerical scheme ensures well-balancing for lake at rest steady states, positivity preservation and entropy stability properties. Moreover, a second-order accurate extension is proposed based on RungeKutta time discretization and piecewise linear limited reconstructions, that preserve the wellbalanced character of the first order scheme. We present several 2D tests assessing the good behaviors of the obtained numerical scheme on unstructured mesh. The numerical scheme seems insensitive to spurious numerical instabilities such as the carbuncle effect.''