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
An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model
Samuel Kokh,Frédéric Lagoutière +1 more
TL;DR: A discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids and properties that ensure a good treatment of the Riemann invariants across the interface are proven.
Journal ArticleDOI
A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography
TL;DR: A finite volume MUSCL scheme for the numerical integration of 2D shallow water equations is presented and the results of a dam-break scenario are presented to show the capability of the numerical model on field-scale applications.
Journal ArticleDOI
Vlasiator: First global hybrid-Vlasov simulations of Earth's foreshock and magnetosheath
S. von Alfthan,Dimitry Pokhotelov,Dimitry Pokhotelov,Yann Kempf,Yann Kempf,Sanni Hoilijoki,Sanni Hoilijoki,Ilja Honkonen,Ilja Honkonen,A. Sandroos,Minna Palmroth +10 more
TL;DR: In this article, a hybrid-Vlasov simulation code, Vlasiator, is proposed for global magnetospheric simulations, which represents ions by a six-dimensional distribution function propagated using a finite volume approach.
Journal ArticleDOI
FEM-FCT - Combining unstructured grids with high resolution
TL;DR: In this paper, the authors presented an extension of flux-corrected transport (FCT) schemes to unstructured grids, where the spatial discretization is performed via finite elements.
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.