University of Leicester
Browse
MA-06-017.pdf (354.38 kB)

High Order WENO Finite Volume Schemes Using Polyharmonic Spline Reconstruction

Download (354.38 kB)
report
posted on 2009-03-02, 12:07 authored by Terhemen Aboiyar, Emmanuil H. Georgoulis, Armin Iske
Polyharmonic splines are utilized in the WENO reconstruction of finite volume discretizations, yielding a numerical method for scalar conservation laws of arbitrary high order. The resulting WENO reconstruction method is, unlike previous WENO schemes using polynomial reconstructions, numerically stable and very flexible. Moreover, due to the theory of polyharmonic splines, optimal reconstructions are obtained in associated native Sobolev-type spaces, called Beppo Levi spaces. This in turn yields a very natural choice for the oscillation indicator, as required in the WENO reconstruction method. The key ingredients of the proposed polyharmonic splineWENO reconstruction algorithm are explained in detail, and one numerical example is given for illustration.

History

Publisher

Dept. of Mathematics. University of Leicester

Available date

2009-03-02

Book series

MA 06-017

Language

en

Usage metrics

    University of Leicester Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC