Linear Kinetic Theory And Particle Transport In Stochastic Mixtures

Pomraning, G. C.

doi:10.1142/9789814343114

Cited by 82 publications

(130 citation statements)

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“…The correlation length is defined in terms of the probability of exit distance ξ from a given phase or mean distance to the complementary phase, introduced [19,20] for models of opacity, and studied [9,12] as a measure of fine scale mixing length. Using this probability measure dξ, we define λ C = ξdξ.…”

Section: An Interfacial Correlation Length Scalementioning

confidence: 99%

Chaos, transport and mesh convergence for fluid mixing

Lim

Glimm

et al. 2008

Acta Math. Appl. Sin. Engl. Ser.

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Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids (as considered here), this interface is defined as a 50% mass concentration isosurface.For shock wave induced (Richtmyer-Meshkov) instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.

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Section: An Interfacial Correlation Length Scalementioning

confidence: 99%

Chaos, transport and mesh convergence for fluid mixing

Lim

Glimm

et al. 2008

Acta Math. Appl. Sin. Engl. Ser.

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“…The equation of atmospheric radiative transfer describes these interactions mathematically. It can be expressed as [15,16]:…”

Section: Atmospheric Radiative Transfer Modelmentioning

confidence: 99%

The influence of temperature on the simulated high resolution spectra of enhanced SCIATRAN model in near infrared band

Liu

Zhang

et al. 2016

Optik

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“…Given that s is in material '; ds k ' is the probability of transition into material k in the distance ds [10]. The total ensemble average of the flux is then defined to be:…”

Section: Governing Equationsmentioning

confidence: 99%

Krylov iterative methods and synthetic acceleration for transport in binary statistical media

Fichtl

Warsa

Prinja

2009

Journal of Computational Physics

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a b s t r a c tIn particle transport applications there are numerous physical constructs in which heterogeneities are randomly distributed. The quantity of interest in these problems is the ensemble average of the flux, or the average of the flux over all possible material 'realizations.' The Levermore-Pomraning closure assumes Markovian mixing statistics and allows a closed, coupled system of equations to be written for the ensemble averages of the flux in each material. Generally, binary statistical mixtures are considered in which there are two (homogeneous) materials and corresponding coupled equations. The solution process is iterative, but convergence may be slow as either or both materials approach the diffusion and/or atomic mix limits. A three-part acceleration scheme is devised to expedite convergence, particularly in the atomic mix-diffusion limit where computation is extremely slow. The iteration is first divided into a series of 'inner' material and source iterations to attenuate the diffusion and atomic mix error modes separately. Secondly, atomic mix synthetic acceleration is applied to the inner material iteration and S 2 synthetic acceleration to the inner source iterations to offset the cost of doing several inner iterations per outer iteration. Finally, a Krylov iterative solver is wrapped around each iteration, inner and outer, to further expedite convergence. A spectral analysis is conducted and iteration counts and computing cost for the new two-step scheme are compared against those for a simple one-step iteration, to which a Krylov iterative method can also be applied.

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Linear Kinetic Theory And Particle Transport In Stochastic Mixtures

Cited by 82 publications

References 0 publications

Chaos, transport and mesh convergence for fluid mixing

Chaos, transport and mesh convergence for fluid mixing

The influence of temperature on the simulated high resolution spectra of enhanced SCIATRAN model in near infrared band

Krylov iterative methods and synthetic acceleration for transport in binary statistical media

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