Assessment of a second-order radiation boundary condition for tidal and wind driven flows

1995 ◽  
pp. 49-70 ◽  
Author(s):  
Matthias Johnsen ◽  
Daniel R. Lynch
Keyword(s):  
Boundary Condition ◽  
Second Order ◽  
Radiation Boundary Condition ◽  
Radiation Boundary

Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain

2013 ◽  
Vol 14 (4) ◽  
pp. 1027-1057 ◽  
Author(s):  
Qiang Ma ◽  
Junzhi Cui
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Second Order ◽  
Asymptotic Model ◽  
Analysis Method ◽  
Radiation Boundary Condition ◽  
Approximation Solution ◽  
Original Solution ◽  
Porous Domain ◽  
Radiation Boundary

AbstractIn this paper a second-order two-scale (SOTS) analysis method 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.

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