In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asympto...In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.展开更多
基金supported by the National Natural Science Foundation of China(90916027)the Special Funds for National Basic Research Program of China(973 Program 2010CB832702)supported by the State Key Laboratory of Science and Engineering Computing.
文摘In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.
