258 research outputs found
A Framework on Moment Model Reduction for Kinetic Equation
By a further investigation on the structure of the coefficient matrix of the
globally hyperbolic regularized moment equations for Boltzmann equation in [Z.
Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571], we propose a
uniform framework to carry out model reduction to general kinetic equations, to
achieve certain moment system. With this framework, the underlying reason why
the globally hyperbolic regularization in [Z. Cai, Y. Fan and R. Li, Comm.
Math. Sci., 11 (2013), pp. 547-571] works is revealed. The even fascinating
point is, with only routine calculation, existing models are represented and
brand new models are discovered. Even if the study is restricted in the scope
of the classical Grad's 13-moment system, new model with global hyperbolicity
can be deduced.Comment: 22 page
13-Moment System with Global Hyperbolicity for Quantum Gas
We point out that the quantum Grad's 13-moment system [R. Yano, Physica A:
Statistical Mechanics and its Applications, 416:231-241, 2014] is lack of
global hyperbolicity, and even worse, the thermodynamic equilibrium is not an
interior point of the hyperbolicity region of the system. To remedy this
problem, by fully considering Grad's expansion, we split the expansion into the
equilibrium part and the non-equilibrium part, and propose a regularization for
the system with the help of the new theory developed in [Z. Cai et al., SIAM J.
Appl. Math., 75(5):2001-2023, 2015, Y. Fan, J. Stat. Phys., 161(4), 2015]. This
provides us a new model which is hyperbolic for all admissible thermodynamic
states, and meanwhile preserves the approximate accuracy of the original
system. It should be noted that this procedure is not a trivial application of
the theory in [Z. Cai et al., SIAM J. Appl. Math., 75(5):2001-2023, 2015, Y.
Fan, J. Stat. Phys., 161(4), 2015].Comment: 23 pages and 12 figure
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