Galerkin Projection and Numerical Integration for a Stochastic Investigation of the Viscous Burgers’ Equation: An Initial Attempt
We consider a stochastic analysis of the non-linear viscous Burgers’ equation and focus on the comparison between intrusive and non-intrusive uncertainty quantification methods. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are applied to a provably stable formulation of the viscous Burgers’ equation, and compared. As measures of comparison: variance size, computational efficiency and accuracy are used.
- 2.S. Hosder, R.W. Walters, R. Perez, A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations. AIAA paper 891 (2006)Google Scholar
- 6.R.C. Smith, Uncertainty Quantification: Theory, Implementation, and Applications, vol. 12 (SIAM, Philadelphia, 2013)Google Scholar