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Efficiency Improvements for Discontinuous Galerkin Finite Element Discretizations of Hyperbolic Conservation Laws

Yeager, Benjamin A
http://rave.ohiolink.edu/etdc/view?acc_num=osu1397231379

Abstract Details

2014, Master of Science, Ohio State University, Civil Engineering.
Discontinuous Galerkin (DG) finite element methods, paired in a method-of-lines approach with an appropriate time stepper, are an increasingly common choice for the numerical solution of hyperbolic conservation laws. They have a number of favorable properties for large-scale modelling of conservative systems, including a high degree of parallelizability, accurate shock capturing, and local conservation; however, they also tend to be computationally expensive in comparison to other common solution techniques. In this work, the computational cost of DG schemes is reduced through the development of new, efficient time steppers and numerical integration rules. New Runge--Kutta, linear multistep, and two-step Runge--Kutta methods are developed that allow for larger stable time steps and higher order accuracy without an overly restrictive time step constraint. New numerical integration rules are constructed specifically for DG spatial discretizations using quadrilateral, triangular, and hexahedral elements, minimizing the total number of function evaluations needed to integrate the DG polynomial approximation over each element. The new methods are then applied to a numerical test case to demonstrate the reduction in computational cost that they afford over existing methods.
Ethan Kubatko, Ph.D. (Advisor)
66 p.
Applied Mathematics; Civil Engineering; Fluid Dynamics
discontinuous Galerkin; Runge--Kutta; linear multistep; two-step Runge--Kutta; numerical integration

Recommended Citations

Citations

  • Yeager, B. A. (2014). Efficiency Improvements for Discontinuous Galerkin Finite Element Discretizations of Hyperbolic Conservation Laws [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397231379

    APA Style (7th edition)

  • Yeager, Benjamin. Efficiency Improvements for Discontinuous Galerkin Finite Element Discretizations of Hyperbolic Conservation Laws. 2014. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1397231379.

    MLA Style (8th edition)

  • Yeager, Benjamin. "Efficiency Improvements for Discontinuous Galerkin Finite Element Discretizations of Hyperbolic Conservation Laws." Master's thesis, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397231379

    Chicago Manual of Style (17th edition)

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