Efficiency of Shock Capturing Schemes for Burgers' Equation with Boundary Uncertainty [chapter]

Per Pettersson, Qaisar Abbas, Gianluca Iaccarino, Jan Nordström
2010 Numerical Mathematics and Advanced Applications 2009  
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
more » ... e 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.
doi:10.1007/978-3-642-11795-4_79 fatcat:qinfetijqjcjtd2pu6wp2y7ufm