Journal ArticleDOI
On the Construction and Comparison of Difference Schemes
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This article is published in SIAM Journal on Numerical Analysis.The article was published on 1968-09-01. It has received 3383 citations till now.read more
Citations
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Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
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
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.
Journal ArticleDOI
The numerical simulation of two-dimensional fluid flow with strong shocks
Paul R. Woodward,Phillip Colella +1 more
TL;DR: In this paper, a comparison of numerical methods for simulating hydrodynamics with strong shocks in two dimensions is presented and discussed, and three approaches to treating discontinuities in the flow are discussed.
Journal ArticleDOI
Towards the Ultimate Conservative Difference Scheme
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
References
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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
Difference schemes for hyperbolic equations with high order of accuracy
Peter D. Lax,Burton Wendroff +1 more
Journal ArticleDOI
A Runge-Kutta for all Seasons
TL;DR: By analyzing the trends over N steps at once, stimates of the accuracy can be derived which compare in reliability with those for classic predictor-corrector methods.