Convergence of single rate and multirate undrained split iterative schemes for a fractured biot model.

This paper considers a coupled flow and mechanics problem in a fractured poro-elastic medium. The fracture geometry is explicitly treated as a possibly non-planar interface. The model equations are of mixed dimensional type where the flow equation on a d − 1 dimensional fracture surface is coupled to a d dimensional porous matrix. An extension of the widely used undrained split iterative coupling scheme to the fractured poro-elastic media is performed. The particularity is in the time-discretization where both the single rate scheme in which flow and mechanics share the exact same time step, and the multirate scheme in which flow takes multiple fine time steps within one coarse mechanics time step. In the coupled model considered here, the fracture flow model is a lubrication-type system (Girault et al. Math. Models Methods Appl. Sci. 25(4):587–645 2015) whereas in the porous matrix the linear quasi-static Biot equations are considered. Convergence analysis of the undrained split iterative scheme and Banach fixed-point contraction type results are obtained that establish the geometric convergence of the scheme and the uniqueness of the obtained solution. [ABSTRACT FROM AUTHOR]