Techniques for the reconstruction of a distribution from a finite number of its moments

John, Volker; Angelov, I.; Öncül, A. A.; Thévenin, Dominique

doi:10.1016/j.ces.2007.02.041

Cited by 182 publications

(129 citation statements)

References 29 publications

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“…The presumed averaged SGS PDFs are computed employing mapped LES moments ðñ; r n Þ and using Eq. (15). As expected, the figure displays the best prediction when a b PDF is used.…”

Section: B Assessment Of the Presumed-pdf Approach For Computing Filsupporting

confidence: 55%

“…However, if the PDF is complex, it has the drawback that it can only be approximately reconstructed by a large number of its moments. 15 It is certainly computationally easier if it can be shown that the PDF of the scalar conforms to a PDF having a simple mathematical form for which only a small number of moments is necessary for its reconstruction. Such simple PDFs are, for example, the Dirac, the Gaussian, and the b functions for which one needs a maximum number of two moments for reconstruction.…”

Section: The Pdf Of the Conserved Scalarmentioning

confidence: 99%

“…The quantity <f sgs c > c is equivalent to a filtered PDF of the scalar as defined by Jiménez et al 3 for incompressible flows and it is given by the mass-weighted PDF of the scalar over planes of height equal to the filter width (coarsened-grid planes). The filtered PDF may be computed as < f sgs c ðn;ñ; r n Þ > c ¼ ð f c ðñ; r n Þf sgs c ðn;ñ; r n Þdñdr n (15) by using the mass-weighted joint-moment PDF f c in conjunction with the PDF f sgs c , defined as a function of couples of moments ðñ; r n Þ instead of x where r n is the moment-space variable representing r Z , and integrating over the LESmoment space ðñ; r n Þ. The definition of Eq.…”

Section: The Pdf Of the Conserved Scalarmentioning

confidence: 99%

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The subgrid-scale scalar variance under supercritical pressure conditions

Masi

Bellan

2011

Physics of Fluids

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To model the subgrid-scale (SGS) scalar variance under supercritical-pressure conditions, an equation is first derived for it. This equation is considerably more complex than its equivalent for atmospheric-pressure conditions. Using a previously created direct numerical simulation (DNS) database of transitional states obtained for binary-species systems in the context of temporal mixing layers, the activity of terms in this equation is evaluated, and it is found that some of these new terms have magnitude comparable to that of governing terms in the classical equation. Most prominent among these new terms are those expressing the variation of diffusivity with thermodynamic variables and Soret terms having dissipative effects. Since models are not available for these new terms that would enable solving the SGS scalar variance equation, the adopted strategy is to directly model the SGS scalar variance. Two models are investigated for this quantity, both developed in the context of compressible flows. The first one is based on an approximate deconvolution approach and the second one is a gradient-like model which relies on a dynamic procedure using the Leonard term expansion. Both models are successful in reproducing the SGS scalar variance extracted from the filtered DNS database, and moreover, when used in the framework of a probability density function (PDF) approach in conjunction with the b-PDF, they excellently reproduce a filtered quantity which is a function of the scalar. For the dynamic model, the proportionality coefficient spans a small range of values through the layer cross-stream coordinate, boding well for the stability of large eddy simulations using this model.

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“…The presumed averaged SGS PDFs are computed employing mapped LES moments ðñ; r n Þ and using Eq. (15). As expected, the figure displays the best prediction when a b PDF is used.…”

Section: B Assessment Of the Presumed-pdf Approach For Computing Filsupporting

confidence: 55%

Section: The Pdf Of the Conserved Scalarmentioning

confidence: 99%

Section: The Pdf Of the Conserved Scalarmentioning

confidence: 99%

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The subgrid-scale scalar variance under supercritical pressure conditions

Masi

Bellan

2011

Physics of Fluids

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“…Reconstructing a probability distribution from knowledge of a finite set of moments is an ill-posed mathematical problem which already has a long history [19], although there has been renewed interest in recent decades [20,21]. The scientific applications are also quite broad: image processing [22], calculating magnetic moments [23], and molecular electronic structure [24].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of the polarization distribution of the Rice-Mele model

Yahyavi

Hetényi

2017

Phys. Rev. A

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We calculate the gauge-invariant cumulants (and moments) associated with the Zak phase in the Rice-Mele model. We reconstruct the underlying probability distribution by maximizing the information entropy and applying the moments as constraints. When the Wannier functions are localized within one unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We show that in the fully dimerized limit the magnitudes of the moments are all equal. In this limit, if the on-site interaction is decreased towards zero, the distribution shifts towards the midpoint of the unit cell, but the overall shape of the distribution remains the same. Away from this limit, if alternate hoppings are finite and the on-site interaction is decreased, the distribution also shifts towards the midpoint of the unit cell, but it does this by changing shape, by becoming asymmetric around the maximum, and by shifting. We also follow the probability distribution of the polarization in cycles around the topologically nontrivial point of the model. The distribution moves across to the next unit cell, its shape distorting considerably in the process. If the radius of the cycle is large, the shift of the distribution is accompanied by large variations in the maximum.

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“…Current versions of Fluent ANSYS are now equipped with DQMOM and QMOM and up to eight moments of the particle size distribution can be calculated. Algorithms have been developed to reconstruct any particle size distribution based on a finite number of moments (de Souza et al, 2010;John et al, 2007). Using these advanced algorithms in combination with CFD-QMOM could allow us to model the droplet size distribution for different hydrodynamic conditions.…”

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confidence: 99%