Splitting schemes with respect to physical processes for double-porosity poroelasticity problems
For researchers in geomechanics and porous media, this provides a stable numerical method for coupled displacement-pressure problems in fractured reservoirs.
The paper develops splitting schemes for solving double-porosity poroelasticity problems, achieving stability through a three-level explicit-implicit scheme with a regularization parameter. Numerical experiments demonstrate accuracy and stability.
We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to physical processes, where transition to a new time level is associated with solving separate problem for the displacements and fluid pressures in pores and fractures. The stability of schemes is achieved by switching to three-level explicit-implicit difference scheme with some of the terms in the system of equations taken from the lower time level and by choosing a weight parameter used as a regularization parameter. The computational algorithm is based on the finite element approximation in space. The investigation of stability of splitting schemes is based on the general stability (well-posedness) theory of operator-difference schemes. A priori estimates for proposed splitting schemes and the standard two-level scheme are provided. The accuracy and stability of considered schemes are demonstrated by numerical experiments.