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  • 1.
    Söderholm, Lars H.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hilbert Fluid Dynamics Equations Expressed in Chapman-Enskog Pressure Tensor and Heat Current2008In: Transport theory and statistical physics, ISSN 0041-1450, E-ISSN 1532-2424, Vol. 37, no 5-7, p. 520-534Article in journal (Refereed)
    Abstract [en]

    The connection between the Chapman-Enskog and Hilbert expansions is investigated in detail. In particular, the fluid dynamics equations of any order in the Hilbert expansion are given in terms of the pressure tensor and heat current of the Chapman-Enskog expansion.

  • 2.
    Söderholm, Lars H.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hybrid Burnett equations: A new method of stabilizing2007In: Transport theory and statistical physics, ISSN 0041-1450, E-ISSN 1532-2424, Vol. 36, no 4-6, p. 495-512Article in journal (Refereed)
    Abstract [en]

    In the original work by Burnett, the pressure tensor and the heat current contain two time derivates. Those are commonly replaced by spatial derivatives using the equations to zero order in the Knudsen number. The resulting conventional Burnett equations were shown by Bobylev to be linearly unstable. In this paper it is shown that the original equations of Burnett have a singularity. A hybrid of the original and conventional equations is constructed and shown to be linearly stable. It contains two parameters, which have to be larger than or equal to some limit values. For any choice of the parameters, the equations agree with each other and with the Burnett equations to second order in Kn, that is, to the accuracy of the Burnett equations. For the simplest choice of parameters the hybrid equations have no third derivative of the temperature, but the inertia term contains second spatial derivatives. For stationary flow, when the term Kn(2) Ma(2) can be neglected, the only difference,from the conventional Burnett equations is the change of coefficients pi(2) -> pi(3), pi(3) -> pi(3).

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