Multiwavelets and outlier detection for troubled-cell indication in discontinuous Galerkin methods

Thea Vuik

Research output: ThesisDissertation (TU Delft)

45 Downloads (Pure)

Abstract

This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: non-physical spurious oscillations are formed close to these discontinuous regions. These oscillations can be prevented by applying a limiter near these regions. One of the difficulties in using a limiter is identifying the difference between a true discontinuity and a local extremum of the approximation. Troubled-cell indicators can help to detect this difference and identify the discontinuous regions (so-called ’troubled cells’) where a limiter should be applied.
In this dissertation, a multiwavelet formulation is used to decompose the DG approximation. The multiwavelet coefficients act as a troubled-cell indicator since they suddenly increase in the neighborhood of a discontinuity. This leads to the definition of a new multiwavelet indicator that detects elements as troubled if the coefficient is large enough in absolute value. Here, a problem-dependent parameter is needed to define the strictness of the indicator. To forgo the reliance on a parameter, a new outlier-detection algorithm is defined that uses boxplot theory. This method can also be applied to different troubled-cell indicators.
Results are shown for regular one-dimensional and tensor-product two-dimensional meshes, as well as for irregular meshes in one dimension and triangular meshes in two dimensions.
Original languageEnglish
QualificationDoctor of Philosophy
Supervisors/Advisors
  • Heemink, A.W., Supervisor
  • Ryan, Jennifer, Advisor
Award date24 Jan 2017
Print ISBNs978-94-92516-24-4
DOIs
Publication statusPublished - 2017

Keywords

  • Runge-Kutta discontinuous Galerkin method
  • high-order methods
  • limiters
  • shock detection
  • multiresolution analysis
  • wavelets
  • multiwavelets
  • troubled cells
  • outlier detection
  • boxplots

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