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LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION

Sun, Weizhou
http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Mathematical Sciences.
This dissertation consists of three parts. In the first part, we briefly review the discontinuous Garlerkin (DG) method and the local discontinuous Garlerkin (LDG) method. We discuss the development of those methods and explain in detail how they can be used to solve various partial differential equations. We use numerical examples to demonstrate the application of the two methods. In the second part, we develop a LDG method for Khokhlov-Zabolotskaya-Kuznet- zov (KZK) equation. L2 stability is proved for the method and several acoustic examples are studied in comparison with results of previous researchers. We show that our method produces more accurate results in some limiting cases of KZK equaiton. In the last part, an energy conserving LDG method is developed for the improved Boussinesq equation. We show that high order accuracy method can be designed. We demonstrate that optimal order accuracy can be achieved for piecewise polynomial base space and present the process we discovered the method. We also apply our algorithm to solitary waves to understand the phenomenon of the propagation of such waves.
Ching-Shan Chou (Advisor)
Ghaith Hiary (Committee Member)
Dongbin Xiu (Committee Member)
98 p.
Mathematics

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Citations

  • Sun, W. (2016). LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905

    APA Style (7th edition)

  • Sun, Weizhou. LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905.

    MLA Style (8th edition)

  • Sun, Weizhou. "LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905

    Chicago Manual of Style (17th edition)

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