Abstract
One of the tasks of geology and geophysics is to establish the relationship between the mechanical external load and the change in the density of complexly organized media, which can include porous media of various types. For this purpose, the theory of porous media introduces the concept of compressibility coefficient, which allows us simplifying mathematical models describing, for example, the flows in such media. One of the options for obtaining the compressibility coefficient is the direct modeling of the deformation of heterogeneous media under various external loads. Within the framework of this work, the heterogeneous multiscale finite element method on polyhedron supports is used for the numerical simulation because porous media, as a rule, are non-periodic and essentially multiscale. This method makes it possible to develop parallel algorithms on the basis of singling out special subdomains (macroelements) from the general domain, in each of which the solution is constructed independently. To ensure the continuity of the stress-strain state in the whole modeling domain, special projectors are formed taking into account the macro- and microstructure of the sample. This approach makes it possible to obtain the results of the required accuracy with a minimum expenditure of computational resources.
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Acknowledgments
This work was carried out with the financial support of Project FWZZ-2022-0030 (porous medium model), Grant of the President of the Russian Federation MK-3230.2022.1.5 (elastic deformation problem).
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Kutishcheva, A.Y., Markov, S.I. (2023). Application of the Heterogeneous Multiscale Finite Element Method for Modelling the Compressibility of Porous Media. In: Jordan, V., Tarasov, I., Shurina, E., Filimonov, N., Faerman, V. (eds) High-Performance Computing Systems and Technologies in Scientific Research, Automation of Control and Production. HPCST 2022. Communications in Computer and Information Science, vol 1733. Springer, Cham. https://doi.org/10.1007/978-3-031-23744-7_5
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