Journal ArticleDOI
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
TLDR
The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is described in this article.Abstract:
The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is expl...read more
Citations
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Tvd algorithms for the solution of the compressible euler equations on unstructured meshes
TL;DR: The essential features of the finite element side-based scheme and the ID TVD approach are described and their numerical implementation is discussed and the solutions of some inviscid flows, obtained by advancing explicitly in time, are presented.
Journal ArticleDOI
Three‐dimensional modelling of steam flush for DNAPL site remediation
TL;DR: In this article, the authors describe techniques for discretizing problems with horizontal wells in a three-dimensional-tetrahedral mesh, and the effectiveness of nonlinear flux limiters for reducing numerical dispersion is discussed.
Journal ArticleDOI
A Hybrid Finite-Element Finite-Volume Method with Embedded Discontinuities for Solute Transport in Heterogeneous Media
TL;DR: This analysis shows that the new scheme removes a first‐order dependence on mesh refinement observed for the continuous method so that coarser meshes can be used for material interfaces.
Journal ArticleDOI
A projection hybrid high order finite volume/finite element method for incompressible turbulent flows
TL;DR: The projection hybrid FV/FE method presented in [1] is extended to account for species transport equations and turbulent regimes are also considered thanks to the k–e model.
Journal ArticleDOI
Un schéma non linéaire anti-dissipatif pour l'équation d'advection linéaire
TL;DR: In this article, a schema anti-dissipatif obtenu par une methode de type ≪ limiteur ≫ non classique is presented, and a conjecture quant au comportement des solutions numeriques en temps long is proposed.
References
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Journal ArticleDOI
Fully multidimensional flux-corrected transport algorithms for fluids
TL;DR: In this paper, the critical flux limiting stage is implemented in multidimensions without resort to time splitting, which allows the use of flux-corrected transport (FCT) techniques in multi-dimensional fluid problems for which time splitting would produce unacceptable numerical results.
Journal ArticleDOI
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
Gary A. Sod,Gary A. Sod +1 more
TL;DR: In this paper, the finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, and Glimm's method, a random choice method, are discussed.
Journal ArticleDOI
Systems of conservation laws
Peter D. Lax,Burton Wendroff +1 more
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
Journal ArticleDOI
Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme
TL;DR: Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms in this paper, where care is taken to keep the scheme in conservation form.
Journal ArticleDOI
Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works
Jay P. Boris,David L. Book +1 more
TL;DR: A class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction,” which yield realistic, accurate results.