Multiscale Parameter Identification Method for Three Dimension Steady Heat Transfer Model of Composite Materials

Abstract:

In this paper, for heat conductivity identification of three dimension steady heat transfer model of composite materials, a new hybrid Tikhonov regularization mixed multiscale finite-element method is present. First the mathematical models of the forward and the coefficient inverse problems are discussed. Then the forward model is solved by mixed multiscale FEM which utilizes the effects of fine-scale heterogeneities through basis functions formulation computed from local heat transfer problems. At last the numerical approximation of inverse coefficient problem is obtained by Tikhonov regularization method.

• Periodical: Advanced Materials Research (Volumes 706-708)
• Pages: 152-157
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.706-708.152
• Online since: June 2013
• Authors: Tang Wei Liu, He Hua Xu, Xue Lin Qiu, Xiao Bin Shi
• Keywords: Composite Material, Multiscale Method, Parameter Identification, Three Dimension Heat Transfer Model

References

[1] Vegard Kippe, Jørg E. Aarnes, Knut-Andreas Lie, A comparison of multiscale methods for elliptic problems in porous media flow, Comput Geosci, 12, 377-398 (2008)

DOI: 10.1007/s10596-007-9074-6

[2] Aarnes, J. and Y. Efendiev, Mixed multiscale finite element methods for stochastic porous media flows, SIAM Journal on Scientific Computing, 30(5), 2319-2339 (2008)

DOI: 10.1137/07070108x

[3] Chu, C. C., Graham, I. G., Hou, T. Y., A new multiscale finite element method for high-contrast elliptic interface problems, Mathematics of Computation (MCOM), 79 (272), 1915-1955 (2010)

DOI: 10.1090/s0025-5718-2010-02372-5

[4] S. Krogstad, K.¨CA. Lie, H. M. Nilsen, J. R. Natvig, B. Skaflestad, and J. E. Aarnes, SINTEF, A Multiscale Mixed Finite-Element Solver for Three-Phase Black-Oil Flow, Society of Petroleum Engineers. SPE 118993,1-13(2009)

DOI: 10.2118/118993-ms

[5] Yalchin Efendiev, Thomas Y. Hou, Multiscale Finite Element Methods: Theory and Applications. Springer. 27-33(2009)

[6] Xiang Ma,Nicholas Zabaras, A stochastic mixed finite element heterogeneous multiscale method for flow in porous media, Journal of Computational Physics, 230,4696-4722(2011)

DOI: 10.1016/j.jcp.2011.03.001

[7] Todd Arbogast, Mixed Multiscale Methods for Heterogeneous Elliptic Problems, Lecture Notes in Computational Science and Engineering, 83,243-283(2012)

DOI: 10.1007/978-3-642-22061-6_8

[8] Wang Bingxian, Xu Dinghua, Ge Meibao, On the Variational Adjoint Method and Numerical Simulation for A Class of Inverse Problems for Nonlinear Parabolic Equations(in Chinese), Journal of Ningxia University(Natural Science Edition), 29(1):9-13(2008)

[9] Huang S X, Han W, Application of regularization ideas in ill-posed problems of ocean variational data assimilation with local observations, International Conference on Inverse Problems, Hongkong (2002)

[10] Wang Yanfei, Computational Methods for Inverse Problems and Their Applications(in Chinese), Beijing, Higher Education Press (2007)

[11] WANG Ze-wen, XU Ding-hua, A Regularization Method of Inverse Problem for Surface Heat Flux(in Chinese), Journal of Nanchang University(Natural Science), 29(3):261-265(2005)

[12] HE Xinguang , REN Li, Adaptive multiscale finite element method for unsaturated flow in heterogeneous porous media I. Numerical scheme(in Chinese), SHUILI XUEBAO, 40(1),38- 45(2009)

[13] XUE Yu-qun, YE Shu-jun, XIE Chun-hong, ZHANG Yun, Application of multi-scale finite element method to simulation of groundwater flow(in Chinese), SHUILI XUEBAO,7,7-13(2004)

[14] Aixiang Huang, TianXiao Zhou, Theories and Methods of Finite Element(I)(in Chinese), Science Press, Beijing, 164-167(2009)

[15] Yu Changming, Numerical Analysis of Heat and Mass Transfer for Porous Materials(in Chinese), TsingHua University Press,Beijing(2011)

[16] Curtis R. Vogel, Computational Methods for Inverse Problem, TsingHua University Press, Beijing (2011)

[17] Tang-Wei Liu, He-Hua Xu, and Xue-Lin Qiu, A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System, ISRN Applied Mathematics, Volume 2012 (2012), 1-10

DOI: 10.5402/2012/202893