Affordable robust moment closures for CFD based on the maximum-entropy hierarchy

McDonald, James G.; Torrilhon, Manuel

doi:10.1016/j.jcp.2013.05.046

Cited by 88 publications

(106 citation statements)

References 30 publications

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“…Still, McDonald & Groth (2009) and McDonald (2010) showed that the maximum entropy closure can be used in a rarefied gas simulation. The mapping from the parameters to the moment is so computationally demanding that precomputed values and interpolation techniques are used to arrive at an implementation useful for computational fluid dynamics (see McDonald & Torrilhon 2013). Ottinger (2005) used a generalized Hamiltonian structure to impose conditions on thermodynamics models.Öttinger (2010b) argued that a 13-moment theory for gases should replace the heat flux variable q i in Equation 5 by…”

Section: Nonlinear Moment Closuresmentioning

confidence: 99%

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Torrilhon

2016

Annu. Rev. Fluid Mech.

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192

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This article discusses the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium. Such a situation typically is present in rarefied or diluted gases, for flows in microscopic settings, or in general whenever the Knudsen number-the ratio between the mean free path of the particles and a macroscopic length scale-becomes significant. The continuum models are based on the stochastic description of the gas by Boltzmann's equation in kinetic gas theory. With moment approximations, extended fluid dynamic equations can be derived, such as the regularized 13-moment equations. Moment equations are introduced in detail, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low-Mach number setting for which both evolution equations and boundary conditions are well established. Conversely, nonlinear, high-speed processes require special closures that are still under development. Current approaches are examined, along with the challenge of computing shock wave profiles based on continuum equations. 429

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Section: Nonlinear Moment Closuresmentioning

confidence: 99%

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Torrilhon

2016

Annu. Rev. Fluid Mech.

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192

158

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“…Another type of methods, which also approximates the Boltzmann equation, is to formulate moment equations from the Boltzmann equation, and then simulate numerically based on the moment equations [30,32,22]. This method was introduced by Grad [15] and is called the "moment method".…”

Section: Introductionmentioning

confidence: 99%

Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models

Cai

Torrilhon

2015

Journal of Computational Physics

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“…The 14-Moment Interpolative Closure As mentioned above, recently an interpolative-type closure based on the maximum-entropy hierarchy has been proposed. 12,23 The velocity weighting vector used for this closure is…”

Section: Iib Maximum-entropy Closuresmentioning

confidence: 99%

“…However, past research has found that this singular nature is advantageous in practical implementation. 12 It produces very large propagation speeds and was found to yield accurate solutions of stationary, one-dimensional, shock structure having smooth transitions, without undesirable sub-shocks, even for high Mach numbers. 12 The effect of the singularity on wave propagation speed is further explored in Section V.A.…”

Section: Iib Maximum-entropy Closuresmentioning

confidence: 99%

“…9, 10 Unfortunately, complications encountered when considering higher-order moments, such as heat transfer, have severely limited the use of these maximum-entropy closures for general non-equilibrium flows. Recently, new, interpolative-type, maximumentropy-based, 5-moment (one-dimensional gas) and 14-moment (three-dimensional gas) closures, initially investigated by McDonald and Groth,11 and expanded upon by McDonald and Torrilhon,12 have been proposed that successfully navigate the aforementioned problems. This study will present numerical results from a further investigation of this new interpolative 14-moment closure technique via a mathematical dispersion analysis of the governing moment transport equations.…”

Section: Introductionmentioning

confidence: 99%

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Application of a Maximum-Entropy-Based 14-Moment Closure for Multi-Dimensional Non-Equilibrium Flows

Tensuda

McDonald

Groth

2015

22nd AIAA Computational Fluid Dynamics Conference

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The predictive capabilities of a new, 14-moment, maximum-entropy-based, interpolative closure are explored for multi-dimensional non-equilibrium flows with heat transfer. Unlike the maximum-entropy closure on which it is based, the interpolative closure provides closed-form expressions for the closing fluxes. While still presenting singular solutions in regions of realizable moment space, the interpolative closure proves to have a large region of hyperbolicity while remaining tractable. Furthermore, its singular nature is deemed advantageous for practical simulations. An implicit finite-volume procedure is proposed and described for the numerical solution of the 14-moment closure on two-dimensional computational domains, followed by a presentation and discussion of the results of a numerical dispersion analysis. Multi-dimensional applications of the closure are then examined for several canonical flow problems in order to provide an assessment of the capabilities of this novel closure for a range of non-equilibrium flows. The computational performance of the implicit solver is compared to a semi-implicit method. The predictive capabilities of the 14-moment interpolative closure were found to surpass those of the 10-moment Gaussian closure. It was also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat flux. The implicit solver showed improved computational performance compared to the previously studied semi-implicit technique.

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Affordable robust moment closures for CFD based on the maximum-entropy hierarchy

Cited by 88 publications

References 30 publications

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Approximation of the linearized Boltzmann collision operator for hard-sphere and inverse-power-law models

Application of a Maximum-Entropy-Based 14-Moment Closure for Multi-Dimensional Non-Equilibrium Flows

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