Riemann Problem for the Euler Equation with Non-Convex Equation of State including Phase Transitions

Dahmen, Wolfgang; Müller, Siegfried; Voß, Alexander

doi:10.1007/3-540-27907-5_7

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…Acoustic wave propagation test problem: experimental order of convergence (EOC) for the three Godunov-type schemes with (and without) the presented limiters. 9 The MP intervals (36a) include the TVD ones (35a) (see Section 5.2.3).…”

Section: Resultsmentioning

confidence: 99%

“…It is a Mie-Grüneisen-type EOS representative of real liquids and solids, but with a quite bizarre C 1 reference potential for which the sign of the fundamental derivative changes twice: this fictitious material will be called the Bizarrium hereafter. Thus its isentropes may smoothly loose their convexity, 1 as it is the case for the van der Waals EOS near a critical point [8,7,34] or for Bethe-Zel'dovich-Thompson (BZT)-fluids [44,9,35]. The present EOS is nevertheless simpler since it naturally satisfies the thermodynamic stability requirements (thus leading to a hyperbolic SCL).…”

Section: Introductionmentioning

confidence: 87%

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Dissipative issue of high-order shock capturing schemes with non-convex equations of state

Heuzé

Jaouen

Jourdren

2009

Journal of Computational Physics

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 87%

Dissipative issue of high-order shock capturing schemes with non-convex equations of state

Heuzé

Jaouen

Jourdren

2009

Journal of Computational Physics

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“…There is a rarefaction wave arising in gas. However, unlike the classical wave which is formed at positive values of the fundamental derivative, in this case, a mixed wave appears, which is reflected in the profile steepness of all parameters [6]. Part of the front corresponding to negative values of G (x < −0.111) is characterized by a greater steepness, which significantly decreases upon passing to the classical flow region (x > −0.111).…”

mentioning

confidence: 89%

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Koroleva¹,

Mishchenkova²,

Tenenev³

et al. 2021

Nelin. Dinam.

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The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

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“…Additionally, it is possible to examine phenomena that arise with non-convex EOSs* [Dah05,Men88,Mül06]. Using the appropriate tabular or analytic non-convex EOS, one can formulate shock tube initial conditions that lead to non-classical structures such as rarefaction shocks and compression fans, which are associated, e.g., with polymorphic phase transitions exhibited by certain metals [Joh99] and geologic materials [Swe90].…”

Section: A 1-d Riemann Problemsmentioning

confidence: 99%

Enhanced verification test suite for physics simulation codes

Kamm¹,

Brock²,

Brandon³

et al. 2008

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Executive SummaryThis document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations. The key points of this document are:• Verification deals with mathematical correctness of the numerical algorithms in a code, while validation deals with physical correctness of a simulation in a regime of interest. This document is about verification.• The current seven-problem Tri-Laboratory Verification Test Suite, which has been used for approximately five years at the DOE WP laboratories, is limited.• Both the methodology for and technology used in verification analysis have evolved and been improved since the original test suite was proposed.• The proposed test problems are in three basic areas:1. Hydrodynamics 2. Transport processes 3. Dynamic strength-of-materials• For several of the proposed problems we provide a "strong sense verification benchmark," consisting of (i) a clear mathematical statement of the problem with sufficient information to run a computer simulation, (ii) an explanation of how the code result and benchmark solution are to be evaluated, and (iii) a description of the acceptance criterion for simulation code results.

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Riemann Problem for the Euler Equation with Non-Convex Equation of State including Phase Transitions

Cited by 10 publications

References 13 publications

Dissipative issue of high-order shock capturing schemes with non-convex equations of state

Dissipative issue of high-order shock capturing schemes with non-convex equations of state

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

Enhanced verification test suite for physics simulation codes

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