Abstract
In this work, we design a multiscale simulation method based on the Generalized Multiscale Finite Element Method (GMsFEM) for numerical modeling of fluid seepage under permafrost condition in heterogeneous soils. The complex multiphysical model consists of the coupled Richards equation and the Stefan problem. These problems often contain heterogeneities due to variations of soil properties. For this reason, we design coarse-grid spaces for the multiphysical problem and design special algorithms for solving the overall problem. A numerical method has been tested on two- and three-dimensional model problems. A a quasi-real geometry with a complex surface is considered for the three-dimensional case. We demonstrate the efficiency and accuracy of the proposed method using several representative numerical results.
Highlights
It is very important to consider the permafrost strata in soils under difficult climatic conditions in the Far North and the Arctic
We introduce some types of upscaling or multiscale methods
At the center of this geometry, there is a pronounced depression through which liquid seeps
Summary
We design and implement Generalized Multiscale Finite Element Method (GMsFEM) for flows into heterogeneous permafrost soils. In [24,25], we have considered a linear heat transfer, where the permeability does not depend on the pressure This simplifies the algorithm as one does not need to iterate and update multiscale basis functions. We consider the nonlinear soil model, which is more realistic In this case, the permeability depends on the pressure and the overall multiscale procedure requires a somewhat different approach. The main idea of GMsFEM is to apply multiscale basis functions to obtain important information in each coarse grid (computational grid) and build a reduced-order model. The paper ends with the conclusions based on the results of calculations
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