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Uncertainty Quantification in Computational Fluid Dynamics pp 295–333Cite as

Essentially Non-oscillatory Stencil Selection and Subcell Resolution in Uncertainty Quantification

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 92))

Abstract

The essentially non-oscillatory stencil selection and subcell resolution robustness concepts from finite volume methods for computational fluid dynamics are extended to uncertainty quantification for the reliable approximation of discontinuities in stochastic computational problems. These two robustness principles are introduced into the simplex stochastic collocation uncertainty quantification method, which discretizes the probability space using a simplex tessellation of sampling points and piecewise higher-degree polynomial interpolation. The essentially non-oscillatory stencil selection obtains a sharper refinement of discontinuities by choosing the interpolation stencil with the highest polynomial degree from a set of candidate stencils for constructing the local response surface approximation. The subcell resolution approach achieves a genuinely discontinuous representation of random spatial discontinuities in the interior of the simplexes by resolving the discontinuity location in the probability space explicitly and by extending the stochastic response surface approximations up to the predicted discontinuity location. The advantages of the presented approaches are illustrated by the results for a step function, the linear advection equation, a shock tube Riemann problem, and the transonic flow over the RAE 2822 airfoil.

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Acknowledgements

This work was supported by the Netherlands Organization for Scientific Research (NWO) and the European Union Marie Curie Cofund Action under Rubicon grant 680-50-1002.

Author information

Authors and Affiliations

  1. Center for Turbulence Research, Stanford University, Building 500, Stanford, CA, 94305-3035, USA

    Jeroen A. S. Witteveen

  2. Center for Mathematics and Computer Science (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Jeroen A. S. Witteveen

  3. Mechanical Engineering, Stanford University, Building 500, Stanford, CA, 94305-3035, USA

    Gianluca Iaccarino

Authors
  1. Jeroen A. S. Witteveen
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  2. Gianluca Iaccarino
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Corresponding author

Correspondence to Jeroen A. S. Witteveen .

Editor information

Editors and Affiliations

  1. Faculty of Aerospace Engineering, TU Delft, Delft, The Netherlands

    Hester Bijl

  2. d' Alembert Institute-CNRS, Université Pierre et Marie Curie - Paris VI, Paris, France

    Didier Lucor

  3. Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

    Siddhartha Mishra

  4. ETH Zürich Seminar für Angewandte Mathematik, Zürich, Switzerland

    Christoph Schwab

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Witteveen, J.A.S., Iaccarino, G. (2013). Essentially Non-oscillatory Stencil Selection and Subcell Resolution in Uncertainty Quantification. In: Bijl, H., Lucor, D., Mishra, S., Schwab, C. (eds) Uncertainty Quantification in Computational Fluid Dynamics. Lecture Notes in Computational Science and Engineering, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-00885-1_7

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