Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow
A novel Lagrangian-based algorithm is presented for tracking a patch of a passive tracer that evolves according to the 3D advection diffusion equation with a general steady velocity. The algorithm is based on approximating the flow locally by a linear one in space, relative to the center of a patch...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | masterThesis |
| منشور في: |
2022
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/14126 https://doi.org/10.26756/th.2022.454 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513476674715648 |
|---|---|
| author | Wehbe, Rawan |
| author_facet | Wehbe, Rawan |
| author_role | author |
| dc.creator.none.fl_str_mv | Wehbe, Rawan |
| dc.date.none.fl_str_mv | 2022-10-25T09:33:08Z 2022-10-25T09:33:08Z 2022 2022-07-25 |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/14126 https://doi.org/10.26756/th.2022.454 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Lebanese American University |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Lagrange equations -- Numerical solutions Diffusion processes Multiphase flow -- Mathematical models Fluid mechanics -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| dc.title.none.fl_str_mv | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | A novel Lagrangian-based algorithm is presented for tracking a patch of a passive tracer that evolves according to the 3D advection diffusion equation with a general steady velocity. The algorithm is based on approximating the flow locally by a linear one in space, relative to the center of a patch moving with the flow. We seek a semi-analytic solution to the corresponding PDE, based on the Anzats that the exact solution assumes a Gaussian form whose contours are ellipsoids whose axes are evolving according to velocity parameters. We assume that the coefficients that govern this evolution are unknown and we prove that they have to satisfy a coupled system of non-linear first order ODEs. The system is solved numerically using an RK4 scheme. We first check the algorithm against special linear flows with known exact analytical solutions. We then apply the algorithm to Ekman flows in two and three dimensions and compare our results in two dimensions to the grid based, finite element solver COMSOL Multiphysics. In a regime where the patch does not grow too much in size, the results of our algorithm, which is significantly faster, show acceptable agreement with COMSOL. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_c1a40bd9ee0bb784e7328d657d9358cc |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/14126 |
| publishDate | 2022 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flowWehbe, RawanLagrange equations -- Numerical solutionsDiffusion processesMultiphase flow -- Mathematical modelsFluid mechanics -- Mathematical modelsLebanese American University -- DissertationsDissertations, AcademicA novel Lagrangian-based algorithm is presented for tracking a patch of a passive tracer that evolves according to the 3D advection diffusion equation with a general steady velocity. The algorithm is based on approximating the flow locally by a linear one in space, relative to the center of a patch moving with the flow. We seek a semi-analytic solution to the corresponding PDE, based on the Anzats that the exact solution assumes a Gaussian form whose contours are ellipsoids whose axes are evolving according to velocity parameters. We assume that the coefficients that govern this evolution are unknown and we prove that they have to satisfy a coupled system of non-linear first order ODEs. The system is solved numerically using an RK4 scheme. We first check the algorithm against special linear flows with known exact analytical solutions. We then apply the algorithm to Ekman flows in two and three dimensions and compare our results in two dimensions to the grid based, finite element solver COMSOL Multiphysics. In a regime where the patch does not grow too much in size, the results of our algorithm, which is significantly faster, show acceptable agreement with COMSOL.1 online resource (xii, 46 leaves): col. ill.Bibliography: leaves 38-42.Lebanese American University2022-10-25T09:33:08Z2022-10-25T09:33:08Z20222022-07-25Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/14126https://doi.org/10.26756/th.2022.454http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/141262023-11-08T13:38:59Z |
| spellingShingle | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow Wehbe, Rawan Lagrange equations -- Numerical solutions Diffusion processes Multiphase flow -- Mathematical models Fluid mechanics -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| status_str | publishedVersion |
| title | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| title_full | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| title_fullStr | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| title_full_unstemmed | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| title_short | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| title_sort | Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow |
| topic | Lagrange equations -- Numerical solutions Diffusion processes Multiphase flow -- Mathematical models Fluid mechanics -- Mathematical models Lebanese American University -- Dissertations Dissertations, Academic |
| url | http://hdl.handle.net/10725/14126 https://doi.org/10.26756/th.2022.454 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |