Scaling Analysis and Self-Similarity of One-Dimensional Transport Process
Convection-diffusion equation has been widely used to model a variety of flow and transport processes in earth sciences, including spread of pollutants in rivers, dispersion of dissolved material in estuaries and coastal waters, flow and transport in porous media, and transport of pollutants in the...
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| Format: | Article |
| Language: | English |
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Bursa Uludag University
2018-04-01
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| Series: | Uludağ University Journal of The Faculty of Engineering |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/pub/uumfd/issue/36268/330886 |
| _version_ | 1797912924064317440 |
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| author | Ali Ercan |
| author_facet | Ali Ercan |
| author_sort | Ali Ercan |
| collection | DOAJ |
| description | Convection-diffusion equation has been widely used to model a variety of
flow and transport processes in earth sciences, including spread of pollutants
in rivers, dispersion of dissolved material in estuaries and coastal waters, flow
and transport in porous media, and transport of pollutants in the atmosphere.
In this study, the conditions under which one-dimensional convection-diffusion
equation becomes self-similar are investigated by utilizing one-parameter Lie
group of point scaling transformations. By the numerical simulations, it is
shown that the one-dimensional point source transport process in an original
domain can be self-similar with that of a scaled domain. In fact, by changing
the scaling parameter or the scaling exponents of the length dimension, one can
obtain several different down-scaled or up-scaled self-similar domains. The
derived scaling relations obtained by the Lie group scaling approach may
provide additional understanding of transport phenomena at different space and
time scales and may provide additional flexibility in setting up physical
models in which one dimensional transport is significant. |
| first_indexed | 2024-04-10T12:03:40Z |
| format | Article |
| id | doaj.art-79ec8ae26efb4ba3a78d95533be3d129 |
| institution | Directory Open Access Journal |
| issn | 2148-4147 2148-4155 |
| language | English |
| last_indexed | 2024-04-10T12:03:40Z |
| publishDate | 2018-04-01 |
| publisher | Bursa Uludag University |
| record_format | Article |
| series | Uludağ University Journal of The Faculty of Engineering |
| spelling | doaj.art-79ec8ae26efb4ba3a78d95533be3d1292023-02-15T16:16:25ZengBursa Uludag UniversityUludağ University Journal of The Faculty of Engineering2148-41472148-41552018-04-0123123524610.17482/uumfd.3308861779Scaling Analysis and Self-Similarity of One-Dimensional Transport ProcessAli Ercan0University of California, DavisConvection-diffusion equation has been widely used to model a variety of flow and transport processes in earth sciences, including spread of pollutants in rivers, dispersion of dissolved material in estuaries and coastal waters, flow and transport in porous media, and transport of pollutants in the atmosphere. In this study, the conditions under which one-dimensional convection-diffusion equation becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. By the numerical simulations, it is shown that the one-dimensional point source transport process in an original domain can be self-similar with that of a scaled domain. In fact, by changing the scaling parameter or the scaling exponents of the length dimension, one can obtain several different down-scaled or up-scaled self-similar domains. The derived scaling relations obtained by the Lie group scaling approach may provide additional understanding of transport phenomena at different space and time scales and may provide additional flexibility in setting up physical models in which one dimensional transport is significant.https://dergipark.org.tr/tr/pub/uumfd/issue/36268/330886lie group transformationsscalingself-similarityconvection-diffusion equationlie grup değişim yöntemiölçekleme analizikendine benzerlikkonveksiyon-difizyon denklemi |
| spellingShingle | Ali Ercan Scaling Analysis and Self-Similarity of One-Dimensional Transport Process Uludağ University Journal of The Faculty of Engineering lie group transformations scaling self-similarity convection-diffusion equation lie grup değişim yöntemi ölçekleme analizi kendine benzerlik konveksiyon-difizyon denklemi |
| title | Scaling Analysis and Self-Similarity of One-Dimensional Transport Process |
| title_full | Scaling Analysis and Self-Similarity of One-Dimensional Transport Process |
| title_fullStr | Scaling Analysis and Self-Similarity of One-Dimensional Transport Process |
| title_full_unstemmed | Scaling Analysis and Self-Similarity of One-Dimensional Transport Process |
| title_short | Scaling Analysis and Self-Similarity of One-Dimensional Transport Process |
| title_sort | scaling analysis and self similarity of one dimensional transport process |
| topic | lie group transformations scaling self-similarity convection-diffusion equation lie grup değişim yöntemi ölçekleme analizi kendine benzerlik konveksiyon-difizyon denklemi |
| url | https://dergipark.org.tr/tr/pub/uumfd/issue/36268/330886 |
| work_keys_str_mv | AT aliercan scalinganalysisandselfsimilarityofonedimensionaltransportprocess |