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    Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations

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    Shi_ku_0099D_13772_DATA_1.pdf (17.96Mb)
    Issue Date
    2014-12-31
    Author
    Shi, Lei
    Publisher
    University of Kansas
    Format
    164 pages
    Type
    Dissertation
    Degree Level
    Ph.D.
    Discipline
    Aerospace Engineering
    Rights
    Copyright held by the author.
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    Abstract
    High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems in the 1st International Workshop on High-Order Methods. For non-smooth problems, solution based hp-adaptations offer the best promise. Adjoint-based adaptive methods have the capability of dynamically distributing computing resources to areas which are important for predicting engineering performance parameters, such as lift or drag. This thesis presents a robust and efficient adjoint-based adaptive high-order differential formulation for the compressible Navier-Stokes equations, which can rapidly determine an accurate estimate of an engineering output within a prescribed error threshold. The flux reconstruction (FR) or the correction procedure via reconstruction (CPR) method used in this work is a high-order differential formulation. We develop a parallel adjoint-based adaptive CPR solver which can work with any element-based error estimate and handle arbitrary discretization orders for mixed elements. First, a dual-consistent discrete form of the CPR method is derived. Then, an efficient and accurate adjoint-based error estimation method for the CPR method is developed and its accuracy and effectiveness are verified for the linear and non-linear partial differential equations (PDE). For anisotropic h-adaptations, we use a local output error sampling procedure to find the optimal refinement option. The current method has been applied to aerodynamic problems. Numerical tests show that significant savings in the number of DOFs can be achieved through the adjoint-based adaptation.
    URI
    http://hdl.handle.net/1808/27533
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    • Engineering Dissertations and Theses [1055]
    • Dissertations [4473]

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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