Mesh adaptation and transfer schemes for discrete fracture propagation in porous materials

This paper presents a numerical procedure for cohesive hydraulic fracture problems in a multiphase system. The transient problem of crack nucleation and/or advancement, with the ensuing topological changes, is solved by successive remeshing and projection of the field variables required in the time marching scheme. The projection is directly applied to the nodal vector of the previous step and is performed by means of a suitable mapping operator which acts on nodal forces and fluxes. This hence ensures 'a priori' the local fulfilment of the balance equations (equilibrium and mass conservation). The resulting procedure is computationally simple; however checks have to be made on its capability of conserving strain energy of the system. The latter property together with the accuracy of the solution is heuristically assessed on the basis of numerical benchmarks.