Regularization of the Burnett Equations via Relaxation

By Shi Jin, Marshall Slemrod. 2001

137 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/169816962f2624c2c2fe52dbba9fda70cf2aec4d

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In Applied Mathematics

In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Globally Hyperbolic Regularization of Grad's Moment System (2011, unknown): “[11, 10, 16, 20].”
Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, background): “By the way, it should be pointed out that equations obtained by keeping “too many” (meaning 3 or 4) terms of the Hilbert or ChapmanEnskog series, like the so-called Burnett or super-Burnett equations, seem to be irrelevant (a discussion of this matter, an ad hoc recipe to fix this problem, and furth”
Regularization of Grad’s 13 moment equations: Derivation and linear analysis (2003, methodology): “With these equations, we have derived the complete set of regularized equations for the 13 variables %;T;vi; ij;qi that consists of the Equations (6, 14, 15, 16 ).”
A review on slip models for gas microflows (2012, methodology): “Some models beyond the N–S equations, such as the Burnett, BGK–Burnett, and super-Burnett models, had been proposed (Zhong et al. 1993; Jin and Slemrod 2001; Struchtrup and Torrilhon 2003; Balakrishnan 2004).”
Regularized 13-moment equations: shock structure calculations and comparison to Burnett models (2004, methodology): “In the following the shock structure profiles of the regularized Burnett equations are not considered, since our numerical method is not directly applicable to the equations in Jin & Slemrod (2001).”
A high-order moment approach for capturing non-equilibrium phenomena in the transition regime (2009, methodology): “This leads to a stable set of 13 governing equations that are weakly parabolic, and a detailed comparison between the R13 and the regularization of Jin & Slemrod (2001) has been performed by Struchtrup (2005).”