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
Sharpening diffuse interfaces with compressible fluids on unstructured meshes
TL;DR: A specific flux limiter is proposed and inserted into conventional MUSCL type schemes, in the frame of the diffuse interface formulation of Saurel et al. (2009), showing significant improvement in interface representation compared to conventional limiters, such as for example Superbee.
Book ChapterDOI
Upwind schemes, multigrid and defect correction for the steady Navier-Stokes equations
TL;DR: For sufficiently smooth grids this flux computation is second-order accurate and the technique applied is central, the directional dependence coming from the cross derivative terms is neglected.
Journal ArticleDOI
A numerical study of the interactions between viscous flow, transport and kinetics in fixed bed reactors
TL;DR: In this paper, a modular method is proposed for the solution of a reduced set of model equations developed for the description of reactive flows in chemical reactors, which can handle real gas and liquid mixtures with variable density as well as constant density fluids.
Journal ArticleDOI
Convergence of finite difference schemes for conservation laws in several space dimensions: a general theory
TL;DR: It is proved that an a priori estimate weaker than a BV estimate is sufficient and several general theorems of convergence are given in the spirit of the Lax-Wendroff theorem.
Essential Elements of Computational Algorithms for Aerodynamic Analysis and Design
TL;DR: In this paper, the authors trace the development of computational fluid dynamics as a tool for aircraft design and discuss the requirements for effective industrial use, and trade-offs between modeling accuracy and computational costs.
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.