Solution of the boundary-contact dynamic problem for strongly viscous incompressible inhomogeneous media in the unbounded region and its application to modeling the geodynamic conditions of the earth’s tectonosphere - Pyatakov, Yuriy Vladislavovich; Kosygin, Vladimir Yurievich (Computational Continuum Mechanics, 2016)
A mathematical formulation of the boundary-contact dynamic problem for the unbounded inhomogeneous region is presented. A highly viscous incompressible inhomogeneous medium is modeled as a set of disparate disjoint subregions, each having constant viscosity. The values of instantaneous velocity vector components and stresses are set to be continuous at the contact areas between the adjacent interconnecting subdomains. Since the boundary of the modeled region representing the unbounded medium is absent, it is assumed that the instantaneous velocity vector and pressure satisfy the diminishing condition at infinity. It is shown that a representation of the velocity component and pressure in the form of a sum of integral expressions for hydrodynamic potentials (volume, simple and double layers) allows one to reduce the solution of the contact problem in the unbounded region to the solution of the system of Fredholm integral equations of the second kind. Because the factors that stand in the system in front of the improper integrals are, in the absolute value, less than unity, then to find the numerical solution of the equations, we can apply a standard method of successive approximations. The solution of the boundary-contact problem is tested on a model example of a situation at which a convergent break begins to form in the Earth’s lithosphere.