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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Journal ArticleDOI
MOCCT: A numerical technique for astrophysical MHD
John F. Hawley,James M. Stone +1 more
TL;DR: In this paper, the authors describe a method of characteristics-constrained transport (MCT) scheme that uses information propagated along Alfven characteristics to compute electromagnetic forces at intermediate time levels for the induction equation and for the Lorentz force.
Journal ArticleDOI
Third order nonoscillatory central scheme for hyperbolic conservation laws
Xu-Dong Liu,Eitan Tadmor +1 more
TL;DR: In this article, a third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented, which is an extension along the lines of the second-order central scheme of Nessyahu and Tadmor.
Journal ArticleDOI
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
TL;DR: In this article, the authors reformulate the problem in the form commonly used for the relaxation schemes to conservation laws by properly combining the stiff component of the convection terms into the relaxation term.
Book ChapterDOI
Convergence of Generalized MUSCL Schemes
TL;DR: Semidiscrete generalizations of the second order extension of Godunov’s scheme, known as the MUSCL scheme, are constructed, starting with any three point “E” scheme, used to approximate scalar conservation laws in one space dimension.
Journal ArticleDOI
DMS cycle in the marine ocean-atmosphere system – a global model study
TL;DR: In this paper, a global coupled ocean-atmosphere modeling system is established to study the production of dimethylsulfide (DMS) in the ocean, the DMS flux to the atmosphere, and the resulting sulfur concentrations in the atmosphere.
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.