High Order Long-Time Accurate Methods for the Stokes-Darcy System and Uncertainty Quantification of Contaminant Transport
The dissertation includes two parts. The first part consists of designing and analyzing high order long-time accurate numerical methods for Stokes-Darcy system. We propose second and third-order efficient and long-time accurate numerical methods, called IMplicit-EXplicit methods (IMEX) for the coupl...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_migr_etd-9692 |
| Summary: | The dissertation includes two parts. The first part consists of designing and analyzing high order long-time accurate numerical methods for Stokes-Darcy system. We propose second and third-order efficient and long-time accurate numerical methods, called IMplicit-EXplicit methods (IMEX) for the coupled Stokes-Darcy system. Although the original continuum Stokes-Darcy PDE system is fully coupled, our algorithm is capable of decoupling the system into two sub-systems so that a single Stokes and a single Darcy system can be computed in a parallel fashion without iteration. All the schemes we proposed are proven to be unconditionally stable and long-time stable. The bound on the error is uniform-in-time, which is among the first of this kind for second and third-order methods of Stokes-Darcy system. Error estimates for the second order Backward-Differentiation scheme are proved. The second part concerns the Uncertainty of Quantification (UQ) of the contaminant transport. We compute the convection-diffusion equation with Streamline Upwind Petrov-Galerkin (SUPG) method. The quantity of interest is acquired using Monte Carlo and Sparse Grid methods in order to study the sensitivity with respect to the random parameters. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Summer Semester 2015. === May 12, 2015. === Contaminant Transport, IMEX, PDE, Stokes Darcy, Uncertainty Quantification === Includes bibliographical references. === Xiaoming Wang, Professor Co-Directing Dissertation; Max Gunzburger, Professor Co-Directing Dissertation; Xiaoqiang Wang, University Representative; Brian Ewald, Committee Member; Nick Cogan, Committee Member. |
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