Adv. Appl. Math. Mech., 13 (2021), pp. 827-849.
Published online: 2021-04
Cited by
- BibTex
- RIS
- TXT
This article presents well-balanced finite volume weighted essentially non-oscillatory (WENO) schemes to solve the shallow water equations (SWEs). Well-balanced schemes are characterized by preservation of the steady state exactly at the discrete level. The well-balanced property is of paramount importance in practical applications where many studied phenomena are regarded as small perturbations to equilibrium states. To achieve the well-balanced property, numerical fluxes presented here are constructed by means of a suitable conservative variables decomposition and the hydrostatic reconstruction idea. This decomposition strategy allows us to realize a novel simple source term approximation. Both rigorous theoretical analysis and extensive numerical examples all verify that the resulting schemes maintain the well-balanced property exactly. Furthermore, numerical results strongly imply that the proposed schemes can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0138}, url = {http://global-sci.org/intro/article_detail/aamm/18753.html} }This article presents well-balanced finite volume weighted essentially non-oscillatory (WENO) schemes to solve the shallow water equations (SWEs). Well-balanced schemes are characterized by preservation of the steady state exactly at the discrete level. The well-balanced property is of paramount importance in practical applications where many studied phenomena are regarded as small perturbations to equilibrium states. To achieve the well-balanced property, numerical fluxes presented here are constructed by means of a suitable conservative variables decomposition and the hydrostatic reconstruction idea. This decomposition strategy allows us to realize a novel simple source term approximation. Both rigorous theoretical analysis and extensive numerical examples all verify that the resulting schemes maintain the well-balanced property exactly. Furthermore, numerical results strongly imply that the proposed schemes can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions.