Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
01 Jul 1979-Journal of Computational Physics (JOURNAL OF COMPUTATIONAL PHYSICS)-Vol. 32, Iss: 1, pp 101-136
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.
About: This article is published in Journal of Computational Physics.The article was published on 1979-07-01. It has received 6630 citations till now. The article focuses on the topics: Godunov's scheme & Godunov's theorem.
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TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
8,174 citations
Book•
01 Jan 2002TL;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.
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.
5,791 citations
Cites background or methods from "Towards the ultimate conservative d..."
...In the next section we start by giving a geometric interpretation for the scalar advection equation, leading to slope-limitermethods of the type pioneered in van Leer’s work [464]– [468]....
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...Leer in a series of papers, [464] through [468], where he developed the approach known as MUSCL (monotonic upstream-centered scheme for conservation laws) for nonlinear conservation laws....
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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.
5,292 citations
01 Jun 1981
TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.
Abstract: A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.
4,220 citations
TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
3,892 citations
References
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4,135 citations
01 Jan 1967
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
Abstract: Keywords: equations : differentielles ; stabilite ; transport ; transfert de chaleur ; mecanique des : fluides ; ondes Reference Record created on 2005-11-18, modified on 2016-08-08
3,449 citations
3,383 citations
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01 Jan 1948
TL;DR: In this article, the authors proposed a method to compressible ecoulement for compressible compressible and supersonique and onde de choc Reference Record created on 2005-11-18, modified on 2016-08-08
Abstract: Keywords: ecoulement : compressible ; ecoulement : supersonique ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08
3,239 citations
Journal Article•
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