• Login
    View Item 
    •   Home
    • Academic Divisions
    • Computer, Electrical and Mathematical Science & Engineering (CEMSE)
    • Applied Mathematics and Computational Science Program
    • View Item
    •   Home
    • Academic Divisions
    • Computer, Electrical and Mathematical Science & Engineering (CEMSE)
    • Applied Mathematics and Computational Science Program
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

    Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    phd_thesis.pdf
    Size:
    5.392Mb
    Format:
    PDF
    Download
    Type
    Dissertation
    Authors
    Hadjimichael, Yiannis cc
    Advisors
    Ketcheson, David I. cc
    Committee members
    Keyes, David E. cc
    Samtaney, Ravi cc
    Tzavaras, Athanasios cc
    Higueras, Inmaculada
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2017-09-30
    Permanent link to this record
    http://hdl.handle.net/10754/625526
    
    Metadata
    Show full item record
    Abstract
    A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions to preserve the total variation of the solution obtained when perturbed methods are applied to boundary value problems. We implement a stable treatment of nonreflecting boundary conditions for hyperbolic problems that allows high order of accuracy and controls spurious wave reflections. Numerical examples with high-order perturbed Runge–Kutta methods reveal that this technique provides a significant improvement in accuracy compared with zero-order extrapolation.
    Citation
    Hadjimichael, Y. (2017). Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs. KAUST Research Repository. https://doi.org/10.25781/KAUST-VG47P
    DOI
    10.25781/KAUST-VG47P
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-VG47P
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; PhD Dissertations; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2022  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.