科研之友
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摘要
For a model with highly varying and multiscale conductivity, its macroscopic conductivity is approximated by using a mortar method. Macroscopic conductivity is useful in forming macroscopic models for porous media flow applications and in the setting of multiscale fast solvers. Many previous studies are based on the following procedure. Microscale models in each small cell are solved independently with an appropriate boundary condition and the solutions from the localized microscale problems are used to approximate the macroscopic conductivity. The size of the small cell and the boundary conditions affect the accuracy of the approximation. In this work, a mortar method is utilized to form localized microscale problems which are less sensitive to the boundary conditions. In addition, a simple and explicit formula for optimally determined macroscopic conductivity is derived by solving a nonlinear minimization problem. No postprocessing is thus required in our approach to calculate the macroscopic conductivity from the solutions of localized microscopic models. The new approach is numerically studied for various test models and compared to existing methods.
- 出版日期2017-5-1
