A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms☆
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A way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance laws by reforming the source terms as nonconservative products and treating them directly in the definition of the numerical fluxes.Abstract:
We propose a way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance laws. In order to reduce the computational cost, we selected the family of flux vector splitting schemes. We reformulate the source terms as nonconservative products and treat them directly in the definition of the numerical fluxes by means of generalized jump relations. This is applied to a 1D shallow water system with topography and to a 2D simplified model of two-phase flows with damping effects. Numerical results and comparisons with a classical centered discretizations scheme are supplied.read more
Citations
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Book
Finite Volume Methods for Hyperbolic Problems
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Journal ArticleDOI
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
TL;DR: A general strategy is described, based on a local hydrostatic reconstruction, that allows a well-balanced scheme to derive from any given numerical flux for the homogeneous problem, whenever the initial solver satisfies some classical stability properties.
Journal ArticleDOI
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
TL;DR: A theoretical framework allowing one to extend some general concepts related to the numerical approximation of 1-d conservation laws to the more general case of first order quasi-linear hyperbolic systems is provided.
Journal ArticleDOI
A kinetic scheme for the Saint-Venant system¶with a source term
Benoît Perthame,Chiara Simeoni +1 more
TL;DR: A numerical scheme to compute Saint-Venant equations with a source term, due to the bottom topography, in a one-dimensional framework which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom.
Journal ArticleDOI
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
TL;DR: A class of schemes of any desired order of accuracy which preserve the lake at rest perfectly are presented, which should have an impact for studying important classes of lake and ocean flows.
References
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Flux-vector splitting for the Euler equations
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