Lower-Dimensional model of the flow and transport processes in thin domains by numerical averaging technique

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dc.contributor.authorVasilyeva, Maria
dc.contributor.authorMbroh, Nana Adjoah
dc.contributor.authorMehrubeoglu, Mehrube
dc.date.accessioned2024-02-29T18:04:29Z
dc.date.available2024-02-29T18:04:29Z
dc.date.issued2023-12-25
dc.description.abstractIn this work, we present a lower-dimensional model for flow and transport problems in thin domains with rough walls. The full-order model is given for a fully resolved geometry, wherein we consider Stokes flow and a time-dependent diffusion–convection equation with inlet and outlet boundary conditions and zero-flux boundary conditions for both the flow and transport problems on domain walls. Generally, discretizations of a full-order model by classical numerical schemes result in very large discrete problems, which are computationally expensive given that sufficiently fine grids are needed for the approximation. To construct a computationally efficient numerical method, we propose a model-order-reduction numerical technique to reduce the full-order model to a lower-dimensional model. The construction of the lower-dimensional model for the flow and the transport problem is based on the finite volume method and the concept of numerical averaging. Numerical results are presented for three test geometries with varying roughness of walls and thickness of the two-dimensional domain to show the accuracy and applicability of the proposed scheme. In our numerical simulations, we use solutions obtained from the finite element method on a fine grid that can resolve the complex geometry at the grid level as the reference solution to the problem.
dc.description.sponsorshipThis research received no external funding.
dc.identifier.citationVasilyeva, M.; Mbroh, N.A.; Mehrubeoglu, M. Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique. Fluids 2024, 9, 4. https://doi.org/10.3390/fluids9010004
dc.identifier.doihttps://doi.org/10.3390/fluids9010004
dc.identifier.urihttps://hdl.handle.net/1969.6/97764
dc.language.isoen_US
dc.rightsCC BY 4.0 DEED Attribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectupscaling
dc.subjectcoarse grid
dc.subjectflow and transport problem
dc.subjectthin domain
dc.titleLower-Dimensional model of the flow and transport processes in thin domains by numerical averaging technique
dc.typeArticle

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