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A Discontinuous Galerkin Finite Element Method Solution of One-Dimensional Richards’ Equation

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2016, Master of Science, Ohio State University, Civil Engineering.
Unsaturated flows in porous media, attributing to hydraulic conductivity, capillary pressure and gravity, are governed by the Richards’ equation. Due to high non-linearity in the relations among it variables, the Richards’ equation does not have a general closed-form solution. Past numerical Richards’ equation solvers were predominantly predicated on conforming finite element methods or finite different methods, of which the requirement on continuity in solutions occasionally led to convergence failure when abrupt change occurs in boundary conditions or in hydraulic properties of the porous media or both. Moreover, past infiltration schemes influenced by different user-defined vertical discretization could produce significantly different runoff partitioning results even with a same set of parameters. In light of such challenges, hereby presented is a one-dimensional numerical Richards’ equation solver based on the discontinuous Galerkin finite element method (DG-FEM) – a class of finite element method that operates on piecewise continuous trial spaces and allows discontinuity in solutions. Such characteristics make DG-FEM solutions fit for high-intensity moisture inputs and natural heterogeneities. This thesis outlines the steps of DG-FEM formulation on a one-dimensional Richards’ equation. Soil moisture readings under laboratory settings were obtained to validate accuracy, while a long term precipitation dataset was used to contrast the capability of this DG-FEM model to that of a Continuous Galerkin (CG) FEM model in handling extreme rainfall events and partitioning runoff.
Gajan Sivandran, Ph.D (Advisor)
Ethan Kubatko, Ph.D (Committee Member)
Yu-Ping Chin, Ph.D (Committee Member)
108 p.

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Citations

  • Xiao, Y. (2016). A Discontinuous Galerkin Finite Element Method Solution of One-Dimensional Richards’ Equation [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461255638

    APA Style (7th edition)

  • Xiao, Yilong. A Discontinuous Galerkin Finite Element Method Solution of One-Dimensional Richards’ Equation. 2016. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1461255638.

    MLA Style (8th edition)

  • Xiao, Yilong. "A Discontinuous Galerkin Finite Element Method Solution of One-Dimensional Richards’ Equation." Master's thesis, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461255638

    Chicago Manual of Style (17th edition)