Well-balanced high-order finite difference methods for systems of balance laws
- Journal Article
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one preserve every stationary solution, those in the second family only preserve a given set of stationary solutions that depend on some parameters. The accuracy, well-balancedness, and conservation properties of the methods are discussed, as well as their application to systems with singular source terms. The strategy is applied to derive third and fifth order well-balanced methods for a linear scalar balance law, Burgers' equation with a nonlinear source term, and for the shallow water model. In particular, numerical methods that preserve every stationary solution or only water at rest equilibria are derived for the latter.(© 2020 Elsevier Inc.) Show more
Journal / seriesJournal of Computational Physics
Pages / Article No.
SubjectSystems of balance laws; High-order methods; Well-balanced methods; Finite difference methods; Weighted essentially non-oscillatory methods; Shallow Water model
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