Paper Info
Title
Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws.
Abstract
In some previous works, the authors have introduced a strategy to develop well-balanced high-order numerical methods for nonconservative hyperbolic systems in the framework of path-conservative numerical methods. The key ingredient of these methods is a well-balanced reconstruction operator, i.e. an operator that preserves the stationary solutions in some sense. A strategy has been also introduced to modify any standard reconstruction operator like MUSCL, ENO, CWENO, etc. in order to be well-balanced. In this article, the specific case of 1d systems of balance laws is addressed and difficulties are gradually introduced: the methods are presented in the simpler case in which the source term does not involve Dirac masses. Next, systems whose source term involves the derivative of discontinuous functions are considered. In this case, the notion of weak solution is discussed and the Generalized Hydrostatic Reconstruction technique is used for the treatment of singular source terms. A technique to preserve the well-balancedness of the methods in the presence of numerical integration is introduced. The strategy is applied to derive first, second and third order well-balanced methods for Burgers’ equation with a nonlinear source term and for the Euler equations with gravity.
Year
DOI
Venue
2020
10.1007/s10915-020-01149-5
Journal of Scientific Computing
Keywords
Field
DocType
Systems of balance laws, Well-balanced methods, Finite volume methods, High order methods, Reconstruction operators, Compressible Euler equations, Gravitational forces
Nonlinear system,Mathematical analysis,Third order,Numerical integration,Weak solution,Operator (computer programming),Numerical analysis,Law,Finite volume method,Euler equations,Mathematics
Journal
Volume
Issue
ISSN
82
2
0885-7474
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Manuel J. Castro120221.36
Carlos Parés235335.30