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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Book
Finite Volume Methods for Hyperbolic Problems
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
ShuChi-Wang,OsherStanley +1 more
TL;DR: This work extends earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes by providing a new simplified expression for the ENO constructio...
Journal ArticleDOI
Uniformly high order accurate essentially non-oscillatory schemes, 111
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
References
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Journal ArticleDOI
Analysis of Embedded Shock Waves Calculated by Relaxation Methods
TL;DR: In this paper, the requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies, and sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator.
Journal ArticleDOI
Stable and entropy satisfying approximations for transonic flow calculations
Björn Engquist,Stanley Osher +1 more
TL;DR: In this article, finite difference approximations for the small disturbance equation of transonic flow are developed and analyzed, and new schemes of the Cole-Murman type are presented fpr which nonlinear stability is proved.
Journal ArticleDOI
Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes
TL;DR: It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation, and entropy satisfying convergence follows for E schemes - those containing more Numbers than Godunov's scheme.
Proceedings ArticleDOI
High resolution applications of the Osher upwind scheme for the Euler equations
S. R. Chakravarthy,S. Osher +1 more
TL;DR: In this article, an upwind finite-difference method for hyperbolic systems of conservation laws, including the Euler equations, is presented for high resolution extension of the Osher scheme to second-order accuracy.