Abstract
Abstract
We consider a stochastic analysis of non-linear viscous fluid flow problems with smooth and sharp gradients in stochastic space. As a representative example we consider the viscous Burgers’ equation and compare two typical intrusive and non-intrusive uncertainty quantification methods. The specific intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The specific non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are compared in terms of error in the estimated variance, computational efficiency and accuracy. This comparison, although not general, provide insight into uncertainty quantification of problems with a combination of sharp and smooth variations in stochastic space. It suggests that combining intrusive and non-intrusive methods could be advantageous.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference18 articles.
1. Abgrall, R., Congedo, P.M.: A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems. J. Comput. Phys. 15(235), 828–845 (2013)
2. Baker, J., Armaou, A., Christofides, P.D.: Nonlinear control of incompressible fluid flow: application to Burgers’ equation and 2D channel flow. J. Math. Anal. Appl. 252(1), 230–255 (2000)
3. Bänsch, E.: Simulation of instationary, incompressible flows. Acta Math. Univ. Comen. 67(1), 101–114 (1998)
4. Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. Courier Corporation, Chelmsford (2007)
5. Eldred, M., Burkardt, J.: Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In: 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 5 Jan 2009, p. 976
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献