An asymptotic preserving scheme for the Kac model of the Boltzmann equation in the diffusion limit

Bennoune, Mounir; Lemou, Mohammed; Mieussens, Luc
November 2009
Continuum Mechanics & Thermodynamics;Nov2009, Vol. 21 Issue 5, p401
Academic Journal
In this article, we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. Formally, this scheme is shown to be uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro�macro decomposition which leads to an equivalent formulation of the Kac model that couples a kinetic equation with macroscopic ones. This method is validated with various test cases and compared to other standard methods.


Related Articles

  • Systematization of relaxation gas dynamics equations. A review. Galkin, V.; Losev, S. // Fluid Dynamics;Aug2010, Vol. 45 Issue 4, p517 

    The phenomenological theory of relaxation gas dynamics equations is outlined for laminar flows of multicomponent reacting gases in an approximation analogous to the Navier-Stokes approximation. A system of general equations of relaxation gas dynamics including the level kinetics equations for...

  • Extension of Ovsyannikov's Analytical Solutions to Transonic Flows. Kurmaeva, K. V.; Titov, S. S. // Journal of Applied Mechanics & Technical Physics;Nov2005, Vol. 46 Issue 6, p780 

    The solution of the equation of the velocity potential of a steady axisymmetric ideal-gas flow in the neighborhood of a given point at the axis of symmetry in the form of a double series in powers of the distance to the axis of symmetry and its logarithm is considered. Recurrent chains of...

  • Features of internal and external flows in high-speed vehicles with a magnetohydrodynamic air-intake. Bezgin, L.; Vatazhin, A.; Gus’kov, O.; Danilov, M.; Kopchenov, V. // Fluid Dynamics;Sep2007, Vol. 42 Issue 5, p828 

    The features of the internal and external flows in high-speed vehicles with a magnetohydrodynamic air-intake ensuring additional deceleration of the supersonic flow are considered. Preliminary investigations carried out earlier showed that this MHD flow control makes it possible significantly to...

  • Non-equilibrium Flows of Reacting Air Components in Nozzles. Bazilevich, S. S.; Sinitsyn, K. A.; Nagnibeda, E. A. // AIP Conference Proceedings;12/31/2008, Vol. 1084 Issue 1, p843 

    The paper presents the results of the investigation of non-equilibrium flows of reacting air mixtures in nozzles. State-to-state approach based on the solution of the equations for vibrational level populations of molecules and atomic concentrations coupled to the gas dynamics equations is used....

  • Energy–Vorticity Theory of Ideal Fluid Mechanics. Névir, Peter; Sommer, Matthias // Journal of the Atmospheric Sciences;Jul2009, Vol. 66 Issue 7, p2073 

    Nambu field theory, originated by Névir and Blender for incompressible flows, is generalized to establish a unified energy–vorticity theory of ideal fluid mechanics. Using this approach, the degeneracy of the corresponding noncanonical Poisson bracket—a characteristic property...

  • Important aspects in the formulation of solid�fluid debris-flow models. Part I. Thermodynamic implications. Hutter, Kolumban; Schneider, Lukas // Continuum Mechanics & Thermodynamics;Jun2010, Vol. 22 Issue 5, p363 

    This article points at some critical issues which are connected with the theoretical formulation of the thermodynamics of solid�fluid mixtures of frictional materials. It is our view that a complete thermodynamic exploitation of the second law of thermodynamics is necessary to obtain the...

  • Application of a Modular Particle-Continuum Method to Partially Rarefied, Hypersonic Flow. Deschenes, Timothy R.; Boyd, Iain D. // AIP Conference Proceedings;5/20/2011, Vol. 1333 Issue 1, p539 

    The Modular Particle-Continuum (MPC) method is used to simulate partially-rarefied, hypersonic flow over a sting-mounted planetary probe configuration. This hybrid method uses computational fluid dynamics (CFD) to solve the Navier-Stokes equations in regions that are continuum, while using...

  • Assessment of thermodynamic models for dense gas dynamics. Guardone, A.; Vigevano, L.; Argrow, B. M. // Physics of Fluids;Nov2004, Vol. 16 Issue 11, p3878 

    The accuracy of thermodynamic models in the computation of nonclassical gasdynamic phenomena is discussed, to investigate their suitability in connection with the design of experimental apparatuses aimed at the observation of nonclassical wavefields. The Soave–Redlich–Kwong and the...

  • The method of moments and the nonequilibrium thermodynamics of rarefied gases. Zhdanov, V. M.; Roldugin, V. I. // Journal of Experimental & Theoretical Physics;Jun98, Vol. 86 Issue 6, p1141 

    A generalized variant of the nonequilibrium thermodynamics of rarefied gases based on the linearized equations of Grad’s method of moments is studied. It is shown that despite the more complicated form of the thermodynamic forces, which include spatial derivatives of the fluxes, entropy...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics