An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

Bourlioux, Anne; Majda, Andrew J.

doi:10.1088/1364-7830/4/2/307

Cited by 17 publications

(22 citation statements)

References 13 publications

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“…All these statistics are important in testing closure strategies for nonpremixed turbulent combustion 26 -29 in an unambiguous fashion and the present models are very useful in that context. 26 It would be interesting to check the structure of the PDFs at large Péclet numbers for scalar intermittency for the wide variety of space-time periodic flows, where homogenization theory is valid. 16 J 1 ͑ t͒ϭ ͵ tЈϭϪϱ tЈϭt e ϪK J 2 ͑ tϪtЈ͒ e iK J Pe ͐ tЈ t w͑s ͒ds R j ͑ tϪtЈ͒dtЈ,…”

Section: Concluding Discussionmentioning

confidence: 99%

Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

Bourlioux

Majda

2002

Physics of Fluids

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The single-point probability distribution function ͑PDF͒ for a passive scalar with an imposed mean gradient is studied here. Elementary models are introduced involving advection diffusion of a passive scalar by a velocity field consisting of a deterministic or random shear flow with a transverse time-periodic transverse sweep. Despite the simplicity of these models, the PDFs exhibit scalar intermittency, i.e., a transition from a Gaussian PDF to a broader than Gaussian PDF with large variance as the Péclet number increases with a universal self-similar shape that is determined analytically by explicit formulas. The intermittent PDFs resemble those that have been found recently in numerical simulations of much more complex models. The examples presented here unambiguously demonstrate that neither velocity fields inducing chaotic particle trajectories with positive Lyapunov exponents nor strongly turbulent velocity fields are needed to produce scalar intermittency with an imposed mean gradient. The passive scalar PDFs in these models are given through exact solutions that are processed in a transparent fashion via elementary stationary phase asymptotics and numerical quadrature of one-dimensional formulas.

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Section: Concluding Discussionmentioning

confidence: 99%

Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

Bourlioux

Majda

2002

Physics of Fluids

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“…However, in the described scenario the Péclet number is of order ǫ −1 (c.f. Bourlioux and Majda [7]) implying that O(L 1 ) = ǫ −1 . So the generic constant C is of order ǫ −1 .…”

Section: A-priori Error Estimatementioning

confidence: 98%

A localized orthogonal decomposition method for semi-linear elliptic problems

2014

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In this paper we propose and analyze a localized orthogonal decomposition (LOD) method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans a low dimensional multiscale space. The basis is assembled by performing localized linear fine-scale computations on small patches that have a diameter of order H log(H −1 ) where H is the coarse mesh size. Without any assumptions on the type of the oscillations in the coefficients, we give a rigorous proof for a linear convergence of the H 1 -error with respect to the coarse mesh size. To solve the arising equations, we propose an algorithm that is based on a damped Newton scheme in the multiscale space.

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“…The sketch of the proof below emphasizes the main contributions to the operator L N in (10). As in the derivation of (6), we first multiply the Fokker-Planck equation (2) by u u u α α α…”

Section: Test Models With Exactly Solvable Conditional Momentsmentioning

confidence: 99%

Non-Gaussian Test Models for Prediction and State Estimation with Model Errors

Branicki

Chen

Majda

2014

Partial Differential Equations: Theory, Control and Approximation

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Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiquitous in applications in contemporary science and engineering where statistical ensemble prediction and real-time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scientific phenomena. Here a class of statistically exactly solvable non-Gaussian test models are introduced where a generalized Feynman-Kac formulation reduces the exact behavior of conditional statistical moments to the solution of inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and combined with information theory to address two important issues in contemporary statistical prediction of turbulent dynamical systems: coarse-grained ensemble prediction in a perfect model and improving long range forecasting in imperfect models. The models discussed here should be useful for many other applications and algorithms for real time prediction and state estimation.

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An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

Cited by 17 publications

References 13 publications

Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

A localized orthogonal decomposition method for semi-linear elliptic problems

Non-Gaussian Test Models for Prediction and State Estimation with Model Errors

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