Liang Xiao, Wang Ruili. Mixed uncertainty quantification and its application in upwind scheme for computational fluid dynamics (CFD)[J]. Explosion And Shock Waves, 2016, 36(4): 509-515.
Citation:
Liang Xiao, Wang Ruili. Mixed uncertainty quantification and its application in upwind scheme for computational fluid dynamics (CFD)[J]. Explosion And Shock Waves, 2016, 36(4): 509-515.
Liang Xiao, Wang Ruili. Mixed uncertainty quantification and its application in upwind scheme for computational fluid dynamics (CFD)[J]. Explosion And Shock Waves, 2016, 36(4): 509-515.
Citation:
Liang Xiao, Wang Ruili. Mixed uncertainty quantification and its application in upwind scheme for computational fluid dynamics (CFD)[J]. Explosion And Shock Waves, 2016, 36(4): 509-515.
Both aleatory uncertainty and epistemic uncertainty exist in the initial and boundary conditions when we numerically solve the CFD with sharp discontinuity. In this paper, mixed uncertainty quantification approaches are developed to deal with this situation. Specifically, the outer level uncertainty is linked to epistemic uncertainties, and the inner uncertainty is linked to aleatory uncertainty. The non-intrusive polynomial chaos method is utilized to cope with the aleatory uncertainties, while the P-box theory is used to deal with the epistemic uncertainties, and the upwind scheme and Riemann solver are used to solve the deterministic system. We apply this method to the Sod problem in the CFD, and acquire preferable effect. This method evaluates the influence of input uncertainty such as density (aleatory uncertainty) and polytrophic exponent (epistemic uncertainty) on the output uncertainty, the efficiency of this method is also proved. This method is also helpful in evaluating the degree of confidence and validation of the result from modeling and simulation by other models.
Roache P J. Verification of codes and calculations[J]. AIAA Journal, 1998, 36(5):696-702. doi: 10.2514/2.457
[2]
Staf A A. Guide for the verification and validation of computational fluid dynamics simulations[M]. Reston: American Institute of Aeronautics and Astronautics, 1998:126-180.
[3]
American Nuclear Society. Guidelines for the verification and validation of scientific and engineering computer programs for the nuclear industry[M]. ANSI/ANS-10.4-1987, 1987: 63-119.
Deng Xiaogang, Zong Wengang, Zhang Laiping, et al. Verification and validation in computational fluid dynamics[J]. Advances in Mechanics, 2007, 37(2):279-288. doi: 10.3321/j.issn:1000-0992.2007.02.011
Wang Ruili, Wen Wanzhi. Advances in verification and validation of modeling and simulation of the complex engineering[J]. Computer Aided Engineering, 2014, 23(4):61-68. http://d.old.wanfangdata.com.cn/Conference/8538180
Liu Quan, Wang Ruili, Lin Zhong, et al. Uncertainty quantification for JWL EOS parameters in explosive numerical simulation[J]. Explosion and Shock Waves, 2013, 33(6):647-654. doi: 10.3969/j.issn.1001-1455.2013.06.014
Liu Quan, Wang Ruili, Lin Zhong. Uncertainty quantification for Lagrange computation using non-intrusive polynomial chaos[J]. Chinese Journal of Solid Mechanics, 2013, 33(suppl):224-233. http://d.old.wanfangdata.com.cn/Conference/8155576
[8]
Oberkampf W L, Roy C. Verification and validation in scientific computing[M]. New York: Cambridge University Press, 2010:241-305.
[9]
水鸿寿.一维流体力学差分方法[M].北京:国防工业出版社, 1998:225-236.
[10]
Xiu Dongbin, Karniadkis G E. The Wiener-Askey polynomial chaos for stochastic differential equations[J]. SIAM Journal on Scientific Computing, 2002, 24(2):619-644. doi: 10.1137/S1064827501387826
[11]
Cameron R H, Martin W T. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals[J]. Annals of Mathematics, 1947, 48(2):385-398. doi: 10.2307/1969178
DownLoad:
