• Login
    View Item 
    •   DSpace@RPI Home
    • Rensselaer Libraries
    • RPI Theses Online (Complete)
    • View Item
    •   DSpace@RPI Home
    • Rensselaer Libraries
    • RPI Theses Online (Complete)
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Stochastic variational multiscale method for error estimation and adaptivity in uncertain transport problems

    Author
    Li, Jason
    View/Open
    179071_Li_rpi_0185E_11270.pdf (57.77Mb)
    Other Contributors
    Sahni, Onkar; Li, Fengyan; Oberai, Assad; Shephard, M. S. (Mark S.);
    Date Issued
    2018-05
    Subject
    Aeronautical engineering
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/2222
    Abstract
    Similarly, a model term is derived to explicitly estimate the error in a local or element-wise fashion. This model term is approximated using the components of the stabilization parameter used in computing the numerical solution, making error estimation computationally inexpensive. We compare the error estimator with either the true error or a reference error from a much finer discretization, with which our error estimator agrees very well both locally and globally. Further, procedures using the local error estimator are designed to drive adaptivity in the physical domain and in the stochastic domain. In the physical domain, we apply mesh adaptation. Likewise, stochastic adaptivity controls the local spectral approximation (i.e., a spatially varying spectral order over the mesh). We propose two schemes for adaptivity and apply them to mesh adaptivity and stochastic adaptivity individually. We demonstrate adaptivity on several transport problems with up to three orders of savings in the number of degrees-of-freedom for a given level of accuracy.; The focus of this work is the formulation and application of an adaptive approach based on the variational multiscale (VMS) method for stochastic PDEs with uncertain input data. Uncertainty leads to complicated solution behavior and features in both the physical and stochastic domains. These features can be local, requiring high resolution in some portions to be accurate, whereas in other portions, a low level of resolution is sufficient. For such problems, we seek adaptive construction of efficient discretizations which selectively have high resolution in portions with complicated solution behavior.; In this approach, we employ finite elements in the spatial domain and spectral approximation (based on generalized polynomial chaos) in the stochastic domain. The stochastic VMS method allows in computing an accurate solution while accounting for the missing or fine scales through a model term. This model term is algebraically approximated in each element using a stochastic stabilization parameter. We demonstrate that our stochastic VMS methodology provides a stable and accurate solution for complex transport problems.;
    Description
    May 2018; School of Engineering
    Department
    Dept. of Mechanical, Aerospace, and Nuclear Engineering;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
    Collections
    • RPI Theses Online (Complete)

    Browse

    All of DSpace@RPICommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    DSpace software copyright © 2002-2022  DuraSpace
    Contact Us | Send Feedback
    DSpace Express is a service operated by 
    Atmire NV