# Moment Closure Approximations of the Boltzmann Equation Based on $$\varphi$$φ-Divergences

@article{Abdelmalik2015MomentCA,
title={Moment Closure Approximations of the Boltzmann Equation Based on \$\$\varphi \$\$$\phi-Divergences}, author={M. R. A. Abdelmalik and E. H. van Brummelen}, journal={Journal of Statistical Physics}, year={2015}, volume={164}, pages={77-104} } • Published 17 March 2015 • Mathematics • Journal of Statistical Physics This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to$$\varphi $$φ-divergences and a corresponding closure procedure based on minimization of$$\varphi$$φ-divergences. The proposed description encapsulates as special cases Grad’s classical closure based on expansion in Hermite polynomials and Levermore’s entropy-based closure. We establish that the… 16 Citations • T. Pichard • Mathematics Kinetic and Related Models • 2022 A closure relation for moments equations in kinetic theory was recently introduced in [38], based on the study of the geometry of the set of moments. This relation was constructed from a projection • Mathematics International Journal of Computational Fluid Dynamics • 2021 The use of moment-closure methods to predict continuum and moderately rarefied flow offers many modelling and numerical advantages over traditional methods. The maximum-entropy family of moment • Computer Science, Physics • 2020 This work proposes numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions and presents a numerical approximation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence. • Mathematics Continuum Mechanics and Thermodynamics • 2019 The rational extended thermodynamics theory describes non-equilibrium phenomena for rarefied gases, and it is usually approximated in the neighborhood of an equilibrium state. Consequently, the • Mathematics Journal of Nonlinear Mathematical Physics • 2022 The paper gives a derivation of a new one-dimensional non-stationary nonlinear system of moment equations, that depend on the flight velocity and the surface temperature of an aircraft. Maxwell • Physics Physical Review Fluids • 2022 We introduce a closure model for coarse-grained kinetic theories of polar active ﬂuids. Based on a quasi-equilibrium approximation of the particle distribution function, the model closely captures • Mathematics Int. J. Math. Math. Sci. • 2022 A one-dimensional nonstationary nonlinear moment system of equations and an approximation of Maxwell’s microscopic boundary condition will be introduced. The flight speed and surface temperature of ## References SHOWING 1-10 OF 64 REFERENCES This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the • Mathematics • 2010 The order-of-magnitude method proposed by Struchtrup (Phys. Fluids 16(11):3921–3934, 2004) is a new closure procedure for the infinite moment hierarchy in kinetic theory of gases, taking into account In this paper we develop a new closure theory for moment approximations in kinetic gas theory and derive hyperbolic moment equations for 13 fluid variables including stress and heat flux. Classical • Mathematics, Physics • 1991 The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equations are based on a Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the • Mathematics • 2002 m moments and of degree$\alpha (ET_m^\alpha)\$. For such theories the entropy principle is still valid only, if the non equilibrium field variables and their derivatives are sufficiently small with
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