  In this paper a problem of numerical simulation of hydraulic fractures is
considered. An efficient algorithm of solution is proposed for the plain strain
model of hydraulic fracturing. The algorithm utilizes a FEM based subroutine to
compute deformation of the fractured material. The flow of generalized
Newtonian fluid in the fracture is modelled in the framework of lubrication
theory. In this way, the architecture of the computational scheme is relatively
simple and enables one to deal with advanced cases of the fractured material
properties and configurations as well as various rheological models of fluid.
In particular, the problems of poroelasticity, plasticity and spatially varying
properties of the fractured material can be analyzed. The accuracy and
efficiency of the proposed algorithm are verified against analytical benchmark
solutions. The algorithm capabilities are demonstrated using the example of the
hydraulic fracture propagating in complex geological settings.
