Continuum Onset Parameter Based on Entropy Gradients Using Boltzmann's H-Theorem

Schrock, Christopher R.; McMullan, Richard J.; Camberos, A.

doi:10.2514/6.2005-967

Cited by 8 publications

(6 citation statements)

References 7 publications

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“…Schrock et al [5] have shown that the location of initial increase in entropy production for a stationary normal shock wave predicted by the Navier-Stokes equations is few mean free paths downstream of the location predicted by the DSMC technique, thereby indicating that the breakdown parameters based on continuum data may fail to capture the non-equilibrium effects completely.…”

Section: Entropy Generation Ratementioning

confidence: 97%

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Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Chigullapalli

Venkattraman

Иванов

et al. 2010

Journal of Computational Physics

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Section: Entropy Generation Ratementioning

confidence: 97%

“…The entropy generation rate based on a kinetic description in terms of the velocity distribution function can be obtained using the moment transfer equation [18]. The final expression [5] for the entropy generation rate based on kinetic theory is given by…”

Section: Entropy Generation Ratementioning

confidence: 99%

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Chigullapalli

Venkattraman

Иванов

et al. 2010

Journal of Computational Physics

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“…al 8 have shown that the increase in entropy production entering the shock is predicted later by the Navier-Stokes equations than by DSMC, showing evidence that breakdown parameters based upon continuum data may fail to capture the initial non-equilibrium effects. Their results also show that at lower Mach numbers, the entropy production spike is of the order of the scatter in the DSMC data, which somewhat shows the ability of this parameter to characterize non-equilibrium onset.…”

Section: Kinetic Theorymentioning

confidence: 99%

Non-Equilibrium Flow Modeling Using High-Order Schemes for the Boltzmann Model Equations

Chigullapalli

Venkattraman

Alexeenko

et al. 2008

40th Thermophysics Conference

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We consider application of higher-order schemes to the Boltzmann model equations with a goal to develop a deterministic computational approach that is accurate and efficient for simulating flows involving a wide range of Knudsen numbers. The kinetic equations are solved for two non-equilibrium flow problems, namely, the structure of a normal shock wave and an unsteady two-dimensional shock tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter as well as a third-order WENO scheme. The normal shock wave solutions using BGK and ES collision models are compared to the DSMC simulations. The solution for unsteady shock tube is compared to the Navier-Stokes simulations at low Knudsen numbers and the rarefaction effects in such flow are also discussed. It is observed that a higher-order flux scheme provides a better convergence rate and, hence, reduces the computational effort. The entropy generation rate is shown to be a very sensitive indicator of the onset of non-equilibrium as well as accuracy of a numerical scheme and consistency of boundary conditions in both flow problems.

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“…Studies of Schrock et al [17][18][19] state that because entropy generation represents non-equilibrium it can be employed as a similar parameter to the Knudsen number. Therefore it will predict the continuum breakdown onset.…”

Section: Entropy Generationmentioning

confidence: 99%

“…Results of their simulation demonstrate significant improvement of stability, as compared to realizations without explicit entropic estimations. Schrock et al [17][18][19] expanded upon the concept of entropy generation as a means of examining the breakdown of the continuum fluid equations in regions of non-equilibrium. They compared the DSMC result with those obtained by numerically integrating the NS equations in normal shock waves.…”

Section: Introductionmentioning

confidence: 99%

Compressibility and rarefaction effects on entropy and entropy generation in micro/nano Couette flow using DSMC

Ejtehadi

Esfahani

Roohi³

2012

J. Phys.: Conf. Ser.

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Abstract. In the present work, compressible flow of argon gas in the famous problem of Couette flow in micro/nano-scale is considered and numerically analyzed using the direct simulation Monte Carlo (DSMC) method. The effects of compressibility and rarefaction on entropy and entropy generation in terms of viscous dissipation and thermal diffusion are studied in a wide range of Mach and Knudsen numbers and the observed physics are discussed. In this regard, we computed entropy by using its kinetic theory formulation in a microscopic way while the entropy generation distribution is achieved by applying a semi-microscopic approach and thoroughly free from equilibrium assumptions. The results of our simulations demonstrated that the entropy profiles are in accordance with the temperature profiles. It is also illustrated that the increase of Mach number will result in non-uniform entropy profiles with increase in the vicinity of the central regions of the channel. Moreover, generation of entropy in all regions of the domain stages clear growth. By contrast, increasing the Knudsen number has inverse effects such as: uniform entropy profiles and a falling off in entropy generation amount throughout the channel.

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Continuum Onset Parameter Based on Entropy Gradients Using Boltzmann's H-Theorem

Cited by 8 publications

References 7 publications

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Non-Equilibrium Flow Modeling Using High-Order Schemes for the Boltzmann Model Equations

Compressibility and rarefaction effects on entropy and entropy generation in micro/nano Couette flow using DSMC

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