Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique
In 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 conditio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/9/1/4 |
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| author | Maria Vasilyeva Nana Adjoah Mbroh Mehrube Mehrubeoglu |
| author_facet | Maria Vasilyeva Nana Adjoah Mbroh Mehrube Mehrubeoglu |
| author_sort | Maria Vasilyeva |
| collection | DOAJ |
| description | In 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. |
| first_indexed | 2024-03-08T10:56:01Z |
| format | Article |
| id | doaj.art-2dd8f6c4fc5c4775bd3d5945e0865152 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-08T10:56:01Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-2dd8f6c4fc5c4775bd3d5945e08651522024-01-26T16:24:34ZengMDPI AGFluids2311-55212023-12-0191410.3390/fluids9010004Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging TechniqueMaria Vasilyeva0Nana Adjoah Mbroh1Mehrube Mehrubeoglu2Department of Mathematics & Statistics, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USADepartment of Mathematics & Statistics, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USADepartment of Engineering, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USAIn 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.https://www.mdpi.com/2311-5521/9/1/4upscalingcoarse gridflow and transport problemthin domain |
| spellingShingle | Maria Vasilyeva Nana Adjoah Mbroh Mehrube Mehrubeoglu Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique Fluids upscaling coarse grid flow and transport problem thin domain |
| title | Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique |
| title_full | Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique |
| title_fullStr | Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique |
| title_full_unstemmed | Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique |
| title_short | Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique |
| title_sort | lower dimensional model of the flow and transport processes in thin domains by numerical averaging technique |
| topic | upscaling coarse grid flow and transport problem thin domain |
| url | https://www.mdpi.com/2311-5521/9/1/4 |
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