Nonlinear Transport Under Uncertainty

  • Mass Per Pettersson
  • Gianluca Iaccarino
  • Jan Nordström
Part of the Mathematical Engineering book series (MATHENGIN)


Burgers’ equation is an interesting and non-linear model problem from which, many results can be extended to other hyperbolic systems, e.g., the Euler equations. In this chapter, a detailed uncertainty quantification analysis is performed for the Burgers’ equation; we employ a spectral representation of the solution in the form of polynomial chaos expansion. The equation is stochastic as a result of the uncertainty in the initial and boundary values. Galerkin projection results in a coupled, deterministic system of hyperbolic equations from which statistics of the solution can be determined. A well-posed stochastic Galerkin formulation is presented and a strongly stable numerical scheme is devised. The effect of missing data is investigated, in terms of both stability of the numerical scheme and accuracy of the numerical solution.


Riemann Problem Shock Speed Polynomial Chaos Polynomial Chaos Expansion Dissipation Operator 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mass Per Pettersson
    • 1
  • Gianluca Iaccarino
    • 2
  • Jan Nordström
    • 3
  1. 1.Uni ResearchBergenNorway
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mathematics Computational MathematicsLinköping UniversityLinköpingSweden

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