A Second-Order Description of Shock Structure

Reese, Jason M.; Woods, L. C.; Thivet, F.; Candel, Sébastien

doi:10.1006/jcph.1995.1062

Cited by 42 publications

(30 citation statements)

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“…Such a fluid is said to be endowed with internal capillarity. Hence, it clearly appears that the introduction of a dependence of the energy of a fluid on its density gradient corresponds to a higher order modeling of it (as it is done in a Chapman-Enskog expansion in gas dynamics, for instance by Reese et al [29]). …”

Section: Thermodynamic Modelingmentioning

confidence: 98%

The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

Jamet¹,

Lebaigue²,

Coutris³

et al. 2001

Journal of Computational Physics

254

149

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Section: Thermodynamic Modelingmentioning

confidence: 98%

The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

Jamet¹,

Lebaigue²,

Coutris³

et al. 2001

Journal of Computational Physics

254

149

View full text Add to dashboard Cite

“…Best known, perhaps, are the Burnett equations (Burnett 1936;Chapman & Cowling 1970;Struchtrup 2005), variants of which have been shown to accurately reproduce the viscous structure of one-dimensional shock waves (Reese et al 1995). Lockerby & Reese (2008) tested a number of different highorder continuum-type equations against a simple low-speed benchmark case with no bounding surfaces.…”

Section: Local Knudsen Numbers Based On the R13 Equationsmentioning

confidence: 99%

Switching criteria for hybrid rarefied gas flow solvers

2009

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Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic near-equilibrium fluxes (i.e. the Navier-Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher order constitutive relations; in this case, we use the R13 equations. The efficacy of our proposed switching criteria is tested within an illustrative hybrid kinetic/Navier-Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

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“…Best known, perhaps, are the Burnett equations (Burnett 1936, Chapman & Cowling 1970, Struchtrup 2005, variants of which have been shown to accurately reproduce the viscous structure of one-dimensional shock waves (Reese et al 1995). Lockerby and Reese (2008) tested a number of different high-order continuum-type equations against a simple low-speed benchmark case with no bounding surfaces.…”

Section: Local Knudsen Numbers Based On the R13 Equationsmentioning

confidence: 99%

Switching Criteria for Hybrid Rarefied Gas Flow Solvers

Lockerby¹,

Struchtrup²,

Reese³

2008

AIP Conference Proceedings

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Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic non-equilibrium fluxes (i.e. the Navier-Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher-order constitutive relations; in this case, we use the R13 equations [Struchtrup & Torrilhon, Phys. Fluids 15(9), 2668-2680]. The efficacy of our proposed switching criteria is tested within an illustrative hybrid BGK/Navier-Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

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A Second-Order Description of Shock Structure

Cited by 42 publications

References 0 publications

The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

Switching criteria for hybrid rarefied gas flow solvers

Switching Criteria for Hybrid Rarefied Gas Flow Solvers

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