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
Compartmental Modeling of Multidimensional Crystallization
TL;DR: In this article, an approach that couples compartmental modeling with high-resolution methods is developed to simulate spatial variations in the crystal size and shape distribution in solution crystallization processes, which enables a more accurate modeling of the effect of secondary nucleation.
Journal ArticleDOI
Resolving frontal structures: on the payoff using a less diffusive but computationally more expensive advection scheme
Knut Barthel,Ute Daewel,Dhanya Pushpadas,Corinna Schrum,Marius Årthun,Marius Årthun,Henning Wehde +6 more
TL;DR: In this article, the shape-preserving total variation diminishing (TVD) advection scheme was used in an ecosystem model to preserve haline stratification in the North Sea, Barents Sea, and Baltic Sea.
Journal ArticleDOI
Radionuclide and colloid transport in the Culebra Dolomite and associated complementary cumulative distribution functions in the 1996 performance assessment for the Waste Isolation Pilot Plant
TL;DR: The presented results indicate that radionuclide and colloid transport in the Culebra Dolomite does not constitute a serious threat to the effectiveness of the WIPP as a disposal facility for transuranic waste.
Journal ArticleDOI
The simulation of gas dynamics in engine manifolds using non-linear symmetric difference schemes
Richard Pearson,D. E. Winterbone +1 more
TL;DR: The symmetric flux limiter due to Davis, based on the total variation diminishing (TVD) criterion, is shown here to avoid such problems and requires similar computational effort to the FCT approach.
Journal ArticleDOI
Numerical boundary conditions for globally mass conservative methods to solve the shallow‐water equations and applied to river flow
TL;DR: The definitive version of this article can be found at:http://www3.interscience.wiley.com/blogs/interscience/2017/08/19/2017-08/20/
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.