The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations
Phillip Colella,Paul R. Woodward +1 more
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TLDR
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.About:
This article is published in Journal of Computational Physics.The article was published on 1984-04-01 and is currently open access. It has received 3892 citations till now. The article focuses on the topics: Godunov's scheme & Godunov's theorem.read more
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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.
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Smoothed particle hydrodynamics
TL;DR: In this article, the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed, focusing on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.
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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.
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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.
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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.
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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.
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Supersonic flow and shock waves
Richard Courant,Kurt Friedrichs +1 more
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
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Finite difference methods for numerical computation of discontinous solutions of the equations of fluid dynamics
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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. IV. A new approach to numerical convection
TL;DR: In this paper, an approach to numerical convection is presented that exclusively yields upstream-centered schemes, which start from a meshwise approximation of the initial-value distribution by simple basic functions, e.g., Legendre polynomials.
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Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
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