Journal ArticleDOI
The Riemann problem for fluid flow of real materials
Ralph Menikoff,Bradley J. Plohr +1 more
TLDR
In this article, the properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically, and additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.Abstract:
The Riemann problem for fluid flow of real materials is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. The properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically. Important properties of these wave curves are determined by three dimensionless variables characterizing the equation of state: the adiabatic exponent $\ensuremath{\gamma}$, the Gr\"uneisen coefficient $\ensuremath{\Gamma}$, and the fundamental derivative $\mathcal{G}$. Standard assumptions on these variables break down near phase transitions. The result is an anomalous wave structure: either shock waves split into multiple waves, or composite waves form. Additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.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
Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II
TL;DR: In this article, Zhou et al. presented the initial condition dependence of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) mixing layers, and introduced parameters that are used to evaluate the level of mixedness and mixed mass within the layers.
Journal ArticleDOI
Numerical Hydrodynamics in Special Relativity
José María Martí,Ewald Müller +1 more
TL;DR: This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD), and particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD.
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Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves
Philippe G. LeFloch,J Novotny +1 more
TL;DR: In this article, the Riemann problem is formulated as a class of linear hyperbolic equations, and the entropy dissipation function is defined as a function of the total variation functional.
Journal ArticleDOI
An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems
TL;DR: In this paper, a shock-capturing approach to multicomponent flow problems is developed for the compressible Euler equations with a stiffened gas equation of state in multiple space dimensions.
References
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Journal ArticleDOI
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.
Journal ArticleDOI
The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations
Phillip Colella,Paul R. Woodward +1 more
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.
Journal Article
Finite difference methods for numerical computation of discontinous solutions of the equations of fluid dynamics
Journal ArticleDOI
A new quotidian equation of state (QEOS) for hot dense matter
TL;DR: The quotidian equation of state (QEOS) as discussed by the authors is a general-purpose model for high-pressure simulation of high pressure phenomena, which can be used for a wide class of materials.