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

Per Pettersson (), Qaisar Abbas (), Gianluca Iaccarino () and Jan Nordström ()
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Per Pettersson: Stanford University, Department of Mechanical Engineering
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

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 737-745 from Springer

Abstract: 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.

Date: 2010
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DOI: 10.1007/978-3-642-11795-4_79

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