Convergence Along Mean Flows

Holding, Thomas; Hutridurga, Harsha; Rauch, Jeffrey

doi:10.1137/16m1068657

Cited by 4 publications

(1 citation statement)

References 35 publications

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“…The method of twoscale convergence with drift as described in the latter reports is more appropriate for purely periodic velocity fields, with no dependence on the macroscopic variable. Therefore, a possible area of interest in the direction of problems with strong convection is the treatment of a more general flow field; specifically, in a locally-periodic setting following the recent work cited in [24] and in the handling of the homogenization problem for multicomponent mass transport [25].…”

Section: Introductionmentioning

confidence: 99%

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Ijioma

Muntean

2018

Quart. Appl. Math.

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We target at the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of coupled system of evolution equations pertinent to filtration combustion.

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Section: Introductionmentioning

confidence: 99%

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Ijioma

Muntean

2018

Quart. Appl. Math.

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Numerical homogenization method for parabolic advection–diffusion multiscale problems with large compressible flows

Abdulle

Huber

2017

Numer. Math.

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We introduce a numerical homogenization method based on a discontinuous Galerkin finite element heterogeneous multiscale method (DG-HMM) to efficiently approximate the effective solution of parabolic advection-diffusion problems with rapidly varying coefficients, large Péclet number and compressible flows. To estimate the missing data of an effective model, numerical upscaling is performed which accurately captures the effects of microscopic solenoidal or gradient flow at a macroscopic scale such as enhancement or depletion of the effective diffusion. For compressible flow with periodic data, we derive sharp a priori error estimates for the macro and micro discretization errors which are robust in the advection dominated regime. Numerical tests confirm the error estimates for problems with periodic data and illustrate the applicability of our method for problems with non-periodic data.

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Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data

Raveendran,

de Bonis,

Cirillo

et al. 2024

Quart. Appl. Math.

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We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem.

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Convergence Along Mean Flows

Cited by 4 publications

References 35 publications

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Fast drift effects in the averaging of a filtration combustion system: A periodic homogenization approach

Numerical homogenization method for parabolic advection–diffusion multiscale problems with large compressible flows

Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data

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