Издатель: Springer International Publishing , Год издания: 2022

Mathematical simulation of deformation processes occurring in fluid-saturated media requires solving multiphysical problems. We consider a multi-physical problem as a system of differential equations with special conjugation conditions for the physical fields on the interfragmentary surfaces. The interfragmentary contact surface between solid and liquid phases is a 1-connected contact surface. Explicit discretization of the interfragmentary contact surfaces leads to an increase in the degrees of freedom. To treat the problem, we propose a hierarchical splitting of physical processes. At the macro-level, the process of elastic deformation is simulated, taking into account the pressure on the inner surface of fluid-saturated pores. At the micro-level, to determine the fluid pressure inside the pores, the Navier-Stokes equations are numerically solved with the external mechanical loading. For coupling the physical fields, we use the matching conditions for the normal components of the stress tensor on the interfragmentary surfaces. Mathematical simulation of the coupled processes of elastic deformation and fluid dynamics is a resource-intensive procedure. In addition, a computational scheme has to take into account the specifics of the multiphysical problem. We propose modified computational schemes of multiscale non-conforming finite element methods.