An improved unified gas-kinetic scheme and the study of shock structures

Xu, Kun; Huang, Juan

doi:10.1093/imamat/hxr002

Cited by 73 publications

(57 citation statements)

References 24 publications

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“…It predicts density profiles in nitrogen with a viscosity index of 0.74; however, the translational temperature profiles are not in good agreement with DSMC results, especially at large Mach numbers (Liu et al 2014). Note that the early rising of the translational temperature in normal shock waves has also been observed when using the Shakhov kinetic model for monatomic gas simulations (Xu & Huang 2011). The reason for this is the use of a single relaxation time τ , while in the Boltzmann equation the relaxation time depends on the molecular velocity.…”

Section: A Kinetic Model For Non-vibrating Polyatomic Gasesmentioning

confidence: 87%

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

White

Scanlon

et al. 2014

J. Fluid Mech.

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A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases is proposed, based on the Rykov model for diatomic gases. We adopt two velocity distribution functions (VDFs) to describe the system state; inelastic collisions are the same as in the Rykov model, but elastic collisions are modelled by the Boltzmann collision operator (BCO) for monatomic gases, so that the overall kinetic model equation reduces to the Boltzmann equation for monatomic gases in the limit of no translational-rotational energy exchange. The free parameters in the model are determined by comparing the transport coefficients, obtained by a Chapman-Enskog expansion, to values from experiment and kinetic theory. The kinetic model equations are solved numerically using the fast spectral method for elastic collision operators and the discrete velocity method for inelastic ones. The numerical results for normal shock waves and planar Fourier/Couette flows are in good agreement with both conventional direct simulation Monte Carlo (DSMC) results and experimental data. Poiseuille and thermal creep flows of polyatomic gases between two parallel plates are also investigated. Finally, we find that the spectra of both spontaneous and coherent Rayleigh-Brillouin scattering (RBS) compare well with DSMC results, and the computational speed of our model is approximately 300 times faster. Compared to the Rykov model, our model greatly improves prediction accuracy, and reveals the significant influence of molecular models. For coherent RBS, we find that the Rykov model could overpredict the bulk viscosity by a factor of two.

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Section: A Kinetic Model For Non-vibrating Polyatomic Gasesmentioning

confidence: 87%

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

White

Scanlon

et al. 2014

J. Fluid Mech.

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“…Despite the fact that the BKG equations are less complicated than the full Boltzmann equation, numerical techniques such as the lattice Boltzmann method or discrete velocity method [51][52][53][54] are typically required to solve them.…”

Section: A the Boltzmann Equationmentioning

confidence: 99%

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Sagert

Bauer

Colbry

et al. 2014

Journal of Computational Physics

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We introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Our code combines advantages of the DSMC and the Point of Closest Approach techniques for solving the collision integral. With that, it achieves high spatial accuracy in simulations of large particle systems while maintaining computational feasibility. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we reproduce hydrodynamic behavior. To demonstrate that our code can retrieve continuum solutions, we perform a test-suite of classic hydrodynamic shock problems consisting of the Sod, the Noh, and the Sedov tests. We find that the results of our simulations which apply millions of test-particles match the analytic solutions well. In addition, we take advantage of the ability of kinetic codes to describe matter out of the continuum regime when applying large particle mean free paths. With that, we study and compare the evolution of shock waves in the hydrodynamic limit and in a regime which is not reachable by hydrodynamic codes.

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“…Recent works on these methods focused on rarefied high-Mach flow can be found in 16,17,19 . An alternative approach is presented in 26,50 . Indeed, the Unified Gas-Kinetic Scheme (UGKS) 26, 50 uses a finite-volume method where the numerical fluxes are based on the solution of the Shakhov model 35 for a monoatomic gas, or the Rykov model 31 for a diatomic gas with rotational non-equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Models and Gas-Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

2016

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Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work analytically defined Gas-Kinetic schemes based on the Shakhov and Rykov models, for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for rarefied gas flows at high velocities it is necessary to take into account the non-equilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models with rotational relaxation is a mandatory first step towards realistic simulations. Compared to previous works of Xu and co-workers the presented scheme is defined directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

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An improved unified gas-kinetic scheme and the study of shock structures

Cited by 73 publications

References 24 publications

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Kinetic Models and Gas-Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

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