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hp discontinuous Galerkin (DG) methods for coastal ocean circulation and transport

Conroy, Colton J.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1417707743

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Civil Engineering.
In this dissertation, we present the development and implementation of a high-order, discontinuous Galerkin (DG), three-dimensional coastal ocean circulation and transport model. The model solves the three-dimensional shallow water equations (SWE) using a DG spatial discretization coupled with explicit Runge-Kutta (RK) time stepping. All the primary variables, including the free surface elevation, are discretized via discontinuous polynomial spaces of arbitrary order. The difficulty of mismatched lateral boundaries that accompanies a discontinuous free surface is overcome through the use of a novel, well-balanced, sigma coordinate system in the vertical, which transforms the bottom boundary and free surface into coordinate surfaces. Novel techniques incorporated by the new model include: a high-order coupling method that evaluates the discrete depth-integrated velocity exactly, the use of a compact convolution kernel made-up of B-splines that filters out errors in the DG discretization and enhances the accuracy and convergence properties of the numerical solution, as well as a so-called modified basis method, which calculates the vertical velocity and the baroclinic pressure force in a high order fashion. Model verification is presented for a number of three-dimensional analytic test cases including flow and transport problems, displaying up to fourth-order convergence for smooth solutions.
Ethan Kubatko, Dr. (Advisor)
Gil Bohrer, Dr. (Committee Member)
Ching-Shan Chou, Dr. (Committee Member)
Gajan Sivandran, Dr. (Committee Member)
264 p.
Applied Mathematics; Civil Engineering
discontinuous Galerkin, coastal ocean circulation, finite element methods, superconvergence

Recommended Citations

Citations

  • Conroy, C. J. (2014). hp discontinuous Galerkin (DG) methods for coastal ocean circulation and transport [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1417707743

    APA Style (7th edition)

  • Conroy, Colton. hp discontinuous Galerkin (DG) methods for coastal ocean circulation and transport. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1417707743.

    MLA Style (8th edition)

  • Conroy, Colton. "hp discontinuous Galerkin (DG) methods for coastal ocean circulation and transport." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1417707743

    Chicago Manual of Style (17th edition)

osu1417707743
323
© 2014, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.