Doctoral Dissertations

Changxin Qiu

Keywords and Phrases

Artificial compressibility method; Decoupling method; Ensemble method; Interface conditions; Navier-Stokes-Darcy

Abstract

"In this research, several decoupling methods are developed and analyzed for approximating the solution of time-dependent Navier-Stokes-Darcy (NS-Darcy) interface problems. This research on decoupling methods is motivated to efficiently solve the complex Stokes-Darcy or NS-Darcy type models, which arise from many interesting real world problems involved with or even dominated by the coupled porous media flow and free flow. We first discuss a semi-implicit, multi-step non-iterative domain decomposition (NIDDM) to solve a coupled unsteady NS-Darcy system with Beavers-Joseph-Saffman-Jones (BJSJ) interface condition and obtain optimal error estimates. Second, a parallel NIDDM is developed to solve unsteady NS-Darcy model with Beavers-Joseph (BJ) interface condition, which is much more complicated than BJSJ interface condition. We overcome the major difficulties in the analysis which arise from nonlinear terms and BJ interface condition. Furthermore, a Lagrange multiplier method is proposed under the framework of the domain decomposition method to overcome the difficulty of non-unique solutions arising from the defective boundary condition. Meanwhile, we propose and analyze an efficient ensemble algorithm, which can significantly improve the computational efficiency, for fast computation of multiple realizations of the stochastic Stokes-Darcy model with a random hydraulic conductivity tensor. Furthermore, we utilize the idea of artificial compressibility, which decouples the velocity and pressure, to construct the decoupled ensemble algorithm to improve computational efficiency further. We prove that the proposed ensemble methods offer long time stability and optimal error estimates under a time-step condition and two parameter conditions"--Abstract, page iii.

Advisor(s)

He, Xiaoming
Jiang, Nan

Committee Member(s)

Singler, John R.
Han, Daozhi
Li, Buyang

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Comments

Ph.D. in Mathematics with Computational and Applied Mathematics Emphasis

Publisher

Missouri University of Science and Technology

Publication Date

Fall 2019

Pagination

ix, 164 pages

Note about bibliography

Includes bibliographic references (pages 152-163).

Rights

© 2019 Changxin Qiu, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11642

Electronic OCLC #

1139525560

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Included in

Mathematics Commons

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