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
Strong Stability-Preserving High-Order Time Discretization Methods
TL;DR: This paper reviews and further develops a class of strong stability-preserving high-order time discretizations for semidiscrete method of lines approximations of partial differential equations, and builds on the study of the SSP property of implicit Runge--Kutta and multistep methods.
Journal ArticleDOI
Total variation diminishing Runge-Kutta schemes
Sigal Gottlieb,Chi-Wang Shu +1 more
TL;DR: A class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in Shu& Osher (1988), suitable for solving hyperbolic conservation laws with stable spatial discretizations is explored, verifying the claim that TVD runge-kutta methods are important for such applications.
Journal ArticleDOI
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: In this paper, a classe de methodes a elements finis de Galerkin discontinues a variation totale bornee for the resolution des lois de conservation, and the convergence of the convergence is studied.
Book ChapterDOI
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
TL;DR: In this paper, the authors describe the construction, analysis, and application of ENO and WENO schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations, where the key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible.
Journal ArticleDOI
Characteristic-based schemes for the euler equations
TL;DR: Understanding of computer codes for aparticular class of problems has advanced some way toward completeness, yet the problems are sufficiently complex that naive numerical techniques can produce disaster, yet sufficiently simple that well-understood physics can be understood.
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.