Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow

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dc.contributor.author Wehbe, Rawan
dc.date.accessioned 2022-10-25T09:33:08Z
dc.date.available 2022-10-25T09:33:08Z
dc.date.copyright 2022 en_US
dc.date.issued 2022-07-25
dc.identifier.uri http://hdl.handle.net/10725/14126
dc.description.abstract 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. en_US
dc.language.iso en en_US
dc.subject Lagrange equations -- Numerical solutions en_US
dc.subject Diffusion processes en_US
dc.subject Multiphase flow -- Mathematical models en_US
dc.subject Fluid mechanics -- Mathematical models en_US
dc.subject Lebanese American University -- Dissertations en_US
dc.subject Dissertations, Academic en_US
dc.title Forward simulation of three-dimensional advection-diffusion using a fundamental solution for a linear flow en_US
dc.type Thesis en_US
dc.term.submitted Summer en_US
dc.author.degree MS in Applied and Computational Mathematics en_US
dc.author.school SAS en_US
dc.author.idnumber 201703546 en_US
dc.author.commembers Habchi, Wassim
dc.author.commembers Touma, Rony
dc.author.department Computer Science And Mathematics en_US
dc.description.physdesc 1 online resource (xii, 46 leaves): col. ill. en_US
dc.author.advisor Issa, Leila
dc.keywords 3D Advection-diffusion en_US
dc.keywords Lagrangian methods en_US
dc.keywords Patch tracking algorithm en_US
dc.keywords Fundamental solution en_US
dc.description.bibliographiccitations Bibliography: leaves 38-42. en_US
dc.identifier.doi https://doi.org/10.26756/th.2022.454
dc.author.email rawan.wehbi@lau.edu en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php en_US
dc.publisher.institution Lebanese American University en_US
dc.author.affiliation Lebanese American University en_US

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