Rigorous upscaling of rough boundaries for reactive flows

K. Kumar, M.H.B. van Helvoort, I.S. Pop

Research output: Book/ReportReportAcademic

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Abstract

We consider a mathematical model for reactive ¿ow in a channel having a rough (periodically oscillating) boundary with both period and amplitude e. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non-linear and multi-valued rates. We provide a rigorous justi¿cation for the upscaling process in which we de¿ne an upscaled problem de¿ned in a simpler domain with ¿at boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments con¿rm the theoretical predictions and illustrate a practical application of this upscaling process.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages21
Publication statusPublished - 2012

Publication series

NameCASA-report
Volume1237
ISSN (Print)0926-4507

Fingerprint

Upscaling
Rough
Dissolution
Unfolding
Diffusion Process
Convection
Nonlinear Model
Reverse
Crystal
Numerical Experiment
Mathematical Model
Prediction
Estimate

Cite this

Kumar, K., van Helvoort, M. H. B., & Pop, I. S. (2012). Rigorous upscaling of rough boundaries for reactive flows. (CASA-report; Vol. 1237). Eindhoven: Technische Universiteit Eindhoven.
Kumar, K. ; van Helvoort, M.H.B. ; Pop, I.S. / Rigorous upscaling of rough boundaries for reactive flows. Eindhoven : Technische Universiteit Eindhoven, 2012. 21 p. (CASA-report).
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Kumar, K, van Helvoort, MHB & Pop, IS 2012, Rigorous upscaling of rough boundaries for reactive flows. CASA-report, vol. 1237, Technische Universiteit Eindhoven, Eindhoven.

Rigorous upscaling of rough boundaries for reactive flows. / Kumar, K.; van Helvoort, M.H.B.; Pop, I.S.

Eindhoven : Technische Universiteit Eindhoven, 2012. 21 p. (CASA-report; Vol. 1237).

Research output: Book/ReportReportAcademic

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Kumar K, van Helvoort MHB, Pop IS. Rigorous upscaling of rough boundaries for reactive flows. Eindhoven: Technische Universiteit Eindhoven, 2012. 21 p. (CASA-report).