Continuum-fracture models of porous media processes: derivation and analysis

Abstract: Mathematical modelling of heterogeneous materials such as granitic rocks requires special treatment of fractures. We present the derivation of the so-called continuum-fracture model for two types of problems: advection-diffusion process (e.g. transport of contaminants or heat) and hydro-mechanical coupling based on Biot’s theory. For the hydro-mechanical problem we distinguish the linear case and the case of contact and shear-dilation conditions at fractures. Existence of weak solutions is established. The problem is discretized by the finite element method and solved using the so-called fixed-stress iterative splitting whose convergence is analyzed.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).