A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation

Our purpose is to derive a hybrid model for particle systems which combines a kinetic description of the fast particles with a fluid description of the thermal ones. In the present work, fast particles will be described through a collisional kinetic equation of Boltzmann-BGK type while thermal particles will be modeled by means of a system of Euler type equations. Then, we construct a numerical scheme for this model. This scheme satisfies exact conservation properties. We validate the approach by presenting various numerical tests.

[1]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[2]  W. Steckelmacher.  Molecular gas dynamics and the direct simulation of gas flows , 1996 .

[3]  Vittorio Romano,et al.  Extended Hydrodynamical Model of Carrier Transport in Semiconductors , 2000, SIAM J. Appl. Math..

[4]  Patrick Le Tallec,et al.  Coupling Boltzmann and Euler equations without overlapping , 1992 .

[5]  H. Grad.  On the kinetic theory of rarefied gases , 1949 .

[6]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases : notes added in 1951 , 1951 .

[7]  J. Perlat.  Modelisation et calcul parallele d'une couche limite cinetique , 1998 .

[8]  H. Grad.  Principles of the Kinetic Theory of Gases , 1958 .

[9]  H. C. Yee,et al.  A class of high resolution explicit and implicit shock-capturing methods , 1989 .

[10]  Luc Mieussens,et al.  DISCRETE VELOCITY MODEL AND IMPLICIT SCHEME FOR THE BGK EQUATION OF RAREFIED GAS DYNAMICS , 2000 .

[11]  F. Rogier,et al.  A direct method for solving the Boltzmann equation , 1994 .

[12]  Pierre Degond,et al.  Hybrid kinetic/fluid models for nonequilibrium systems , 2003 .

[13]  S. Parker,et al.  A fully nonlinear characteristic method for gyrokinetic simulation , 1993 .

[14]  Kenichi Nanbu,et al.  Direct Simulation Scheme Derived from the Boltzmann Equation. IV. Correlation of Velocity , 1981 .

[15]  Mikhail Naumovich Kogan,et al.  Rarefied Gas Dynamics , 1969 .

[16]  I. Müller,et al.  Rational Extended Thermodynamics , 1993 .

[17]  Bruno Dubroca,et al.  Prise en compte d'un fort déséquilibre cinétique par un modèle aux demi-moments , 2002 .

[18]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[19]  M. De.  Handbuch der Physik , 1957 .

[20]  Patrick Le Tallec,et al.  Coupling Boltzmann and Navier-Stokes Equations by Half Fluxes , 1997 .

[21]  Pierre Degond,et al.  Polynomial upwind schemes for hyperbolic systems , 1999 .

[22]  David B. Goldstein,et al.  Investigations of the motion of discrete-velocity gases , 1988 .

[23]  C. D. Levermore,et al.  Moment closure hierarchies for kinetic theories , 1996 .

[24]  Kazuo Aoki,et al.  Numerical Analysis of a Supersonic Rarefied Gas Flow past a Flat Plate at an Angle of Attack , 1996 .

[25]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[26]  P. Degond,et al.  Turbulence Models for Incompressible Fluids Derived from Kinetic Theory , 2002 .

[27]  J. Krommes,et al.  Linear delta-f simulations of nonlocal electron heat transport , 2000 .

[28]  Michael Junk,et al.  MAXIMUM ENTROPY FOR REDUCED MOMENT PROBLEMS , 2000 .

[29]  C. Buet,et al.  A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics , 1996 .

[30]  Nicolas Crouseilles.  Dérivation de modèles couplés dérive-diffusion/cinétique par une méthode de décomposition en vitesse , 2002 .

[31]  P. Le Tallec,et al.  COUPLING KINETIC MODELS WITH NAVIER-STOKES EQUATIONS , 1998 .