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Efficiency of Shock Capturing Schemes for Burgers’ Equation with Boundary Uncertainty

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Per Pettersson

    (Stanford University, Department of Mechanical Engineering
    Uppsala University, Department of Information Technology, Scientific Computing)

  • Qaisar Abbas

    (Uppsala University, Department of Information Technology, Scientific Computing)

  • Gianluca Iaccarino

    (Stanford University, Department of Mechanical Engineering)

  • Jan Nordström

    (Uppsala University, Department of Information Technology, Scientific Computing
    University of the Witvatersrand, School of Mechanical, Industrial and Aeronautical Engineering
    FOI, The Swedish Defense Research Agency, Department of Aeronautics and Systems Integration)

Abstract

Burgers’ equation with uncertain initial and boundary conditions is approximated using a polynomial chaos expansion approach where the solution is represented as a series of stochastic, orthogonal polynomials. Even though the analytical solution is smooth, a number of discontinuities emerge in the truncated system. The solution is highly sensitive to the propagation speed of these discontinuities. High-resolution schemes are needed to accurately capture the behavior of the solution. The emergence of different scales of the chaos modes require dissipation operators to yield accurate solutions. We will compare the results using the MUSCL scheme with previously obtained results using conventional one-sided operators.

Suggested Citation

  • Per Pettersson & Qaisar Abbas & Gianluca Iaccarino & Jan Nordström, 2010. "Efficiency of Shock Capturing Schemes for Burgers’ Equation with Boundary Uncertainty," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 737-745, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_79
    DOI: 10.1007/978-3-642-11795-4_79
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