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Stability Analysis of Implicit-Explicit Runge-Kutta Discontinous Galerkin Methods for Convection-Dispersion Equations

Hunter, Joseph William
http://rave.ohiolink.edu/etdc/view?acc_num=osu1618655937007128

Abstract Details

2021, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
The purpose of this thesis is to analyze the stability of implicit-explicit Runge-Kutta (IMEX RK) methods when paired with the discontinuous Galerkin method. The analysis of this full discrete spatial-temporal discretization is performed on a linear convection-dispersion equation. The stability analysis is done on a uniform mesh using periodic boundary conditions with the aid of the Fourier method. Five different second or third order IMEX RK methods were studied in this thesis, and each of them is numerically stable under the CFL condition Δt/Δx≤C with some suitable constant C. Different IMEX RK methods lead to different value of this constant C. In addition, how the size of this time-step restriction constant C changed as the dispersion coefficient changes was also studied. The expectation was as the dispersion coefficient became large, so would the time-step restriction. Numerical results showed the value of the time-step restriction could approach zero, become constant, or become increasingly large, depending on the specific IMEX RK method.
Yulong Xing (Advisor)
Yuan Lou (Committee Member)
75 p.
Mathematics
Discontinuous Galerkin method; IMEX; PDE; Runge-Kutta; stability analysis

Recommended Citations

Citations

  • Hunter, J. W. (2021). Stability Analysis of Implicit-Explicit Runge-Kutta Discontinous Galerkin Methods for Convection-Dispersion Equations [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618655937007128

    APA Style (7th edition)

  • Hunter, Joseph. Stability Analysis of Implicit-Explicit Runge-Kutta Discontinous Galerkin Methods for Convection-Dispersion Equations. 2021. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1618655937007128.

    MLA Style (8th edition)

  • Hunter, Joseph. "Stability Analysis of Implicit-Explicit Runge-Kutta Discontinous Galerkin Methods for Convection-Dispersion Equations." Master's thesis, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618655937007128

    Chicago Manual of Style (17th edition)

osu1618655937007128
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This open access ETD is published by The Ohio State University and OhioLINK.