Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equation in Plane and Axisymmetric Geometries

Mieussens, Luc

doi:10.1006/jcph.2000.6548

Cited by 337 publications

(265 citation statements)

References 28 publications

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“…SMOKE is a parallel code based on conservative numerical schemes developed by L. Mieussens [12]. A second order spatial discretization with axial symmetry is used along with implicit time integration.…”

Section: Finite Volume Methods For Bgk and Es-bgk Equationsmentioning

confidence: 99%

Analysis of Different Approaches to Modeling of Nozzle Flows in the Near Continuum Regime (Preprint)

Титов¹,

Kumar²,

Levin³

et al. 2008

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)Air Force Research Laboratory (AFMC) AFRL/RZS SPONSOR/MONITOR'S Pollux Drive NUMBER(S)Edwards AFB CA 93524-7048 AFRL-RZ-ED-TP-2008-285 DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution unlimited (PA #08274A). SUPPLEMENTARY NOTESFor presentation at the 26 th International Symposium on Rarefied Gas Dynamics, Kyoto, Japan, 21-25 July 2008. ABSTRACTConical nozzle flows are studied for Reynolds numbers of 1,230 and 12,300 using different numerical techniques: DSMC Method, Navier-Stokes/CFD accounting for velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of BGK equation. Detailed comparisons of the stability accuracy, and convergence of the employed numerical techniques provide better understanding of their benefits and deficiencies and assists in selecting the most appropriate technique for a particular nozzle and flow application. The deterministic and statistical solutions of the BGK equation were found to be in good agreement with the benchmark DSMC results. The Navier-Stokes solution differs from the DSMC in the boundary layer. Abstract. Conical nozzle flows are studied for Reynolds numbers of 1,230 and 12,300 using different numerical techniques: DSMC Method, Navier-Stokes/CFD accounting for velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of BGK equation. Detailed comparisons of the stability, accuracy, and convergence of the employed numerical techniques provides better understanding of their benefits and deficiencies, and assists in selecting the most appropriate technique for a particular nozzle and flow application. The deterministic and statistical solutions of the BGK equation were found to be in good agreement with the benchmark DSMC results. The Navier-Stokes solution differs from DSMC in the boundary layer.

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Section: Finite Volume Methods For Bgk and Es-bgk Equationsmentioning

confidence: 99%

Analysis of Different Approaches to Modeling of Nozzle Flows in the Near Continuum Regime (Preprint)

Титов¹,

Kumar²,

Levin³

et al. 2008

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“…In this section we derive a numerical scheme for the coupled kinetic -hydrodynamic system (24). We start introducing a first order time splitting algorithm and we continue with a detailed description of the relaxation and transport steps in each subdomain.…”

Section: The Coupled Numerical Schemementioning

confidence: 99%

“…In [23] and [24], it is proven that such a discrete equilibrium distribution can be built for the standard BGK and for the ES-BGK equations. With the discrete equilibrium G f implicitly defined in (33) macroscopic density, momentum and energy are exactly conserved by the numerical scheme.…”

Section: Relaxation Step In Es-bgk Cellsmentioning

confidence: 99%

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

Alaia

Puppo

2012

Journal of Computational Physics

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In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used to represent the transition between fully kinetic to equilibrium flows.In this fashion, the Boltzmann solver is used only when the collision integral is non-stiff, and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities. Thus, in principle, the same mesh size and time steps can be used in the whole computation. Moreover, the time step is limited only by convective terms.Since the Boltzmann solver is applied only in wholly kinetic regimes, we use the reduced noise DSMC scheme we have proposed in Part I of the present work. This ensures a smooth exchange of information across the different domains, with a natural way to construct interface numerical fluxes. Several tests comparing our hybrid scheme with full Boltzmann DSMC computations show the good agreement between the two solutions, on a wide range of Knudsen numbers.

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“…(9) have been formulated 14,16,17 such that the positivity of the entropy generation rate due to collisional relaxation, Eq. (12), is strictly enforced.…”

Section: Ivc Calculation Of Entropy Generation Ratementioning

confidence: 99%

Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations

Chigullapalli

Venkattraman

Alexeenko

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The viscous effects on unsteady shock wave propagation are investigated by numerical solution of the Boltzmann model kinetic equations. The kinetic equations are solved for two unsteady non-equilibrium flow problems, namely, the one-dimensional Riemann problem and a two-dimensional viscous shock-tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space using various flux schemes. The discrete version of H-theorem is applied for analysis of accuracy of the numerical solution as well as of the onset of non-equilibrium. Simulations show that the maximum entropy generation rate in viscous shock tube occurs in the boundary layer / shock wave interaction region. The entropy generation rate is used to determine the time-variation of the speed of propagation of shock, contact discontinuity and rarefaction waves.

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Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equation in Plane and Axisymmetric Geometries

Cited by 337 publications

References 28 publications

Analysis of Different Approaches to Modeling of Nozzle Flows in the Near Continuum Regime (Preprint)

Analysis of Different Approaches to Modeling of Nozzle Flows in the Near Continuum Regime (Preprint)

A hybrid method for hydrodynamic-kinetic flow – Part II – Coupling of hydrodynamic and kinetic models

Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations

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