Maximum entropy based finite element analysis of porous media

Abstract

The maximum entropy theory has been used in a wide variety of physical, mathematical and engineering applications in the past few years. However, its application in numerical methods, especially in developing new shape functions, has attracted much interest in recent years. These shape functions possess the potential for performing better than the conventional basis functions in problems with randomly generated coarse meshes. In this paper, the maximum entropy theory is adopted to spatially discretize the deformation variable of the governing coupled equations of porous media. This is in line with the well-known fact that higher-order shape functions can provide more stable solutions in porous problems. Some of the benchmark problems in deformable porous media are solved with the developed approach and the results are compared with available references.

Keywords

maximum entropy FEM / fully coupled multi-phase system / porous media

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The authors gratefully acknowledge the High Performance Computing Laboratory (HPC Lab), University of Tehran for the technical support. The authors wish to express their thanks to Professor N. Sukumar for his maximum entropy code. The financial support of Iran National Science Foundation (INSF) is gratefully ackonwledged.

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