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
Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach
TL;DR: This paper proves the convergence of a class of explicit and high-order accurate finite difference schemes for scalar nonlinear hyperbolic conservation laws in several space dimensions by applying the general method presented elsewhere.
Journal ArticleDOI
Biomimetic spiroid winglets for lift and drag control
TL;DR: In this article, a biomimetic abstraction of the principle behind a bird's wingtip feathers was applied to study spiroid wingtips, which look like an extended blended wingtip that bends upward by 360 degrees to form a large rigid ribbon.
Journal ArticleDOI
Positive schemes for solving multi-dimensional hyperbolic systems of conservation laws II
Xu-Dong Liu,Peter D. Lax +1 more
TL;DR: This paper shows that the scheme of Kurganov and Tadmor is positive in the sense of Friedrichs for systems as well, and presents the scheme as a convex combination of composites of positive schemes.
Journal ArticleDOI
A multiple marker level-set method for simulation of deformable fluid particles
TL;DR: In this paper, a multiple marker level-set method is introduced for direct numerical simulation of deformable fluid particles (bubbles and droplets), which is integrated in a finite-volume framework on collocated unstructured grids.
Journal ArticleDOI
Model Validation: Model Parameter and Measurement Uncertainty
TL;DR: The methodology is presented to incorporate measurement and model parameter uncertainty in a metric for model validation through a weighted r 2 norm and the results show that the metric presented can discriminate between valid and invalid models.
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.