Geodesic
A software package for the mathematical simulation of fracture in a thermo-poroelastic medium
Numerical methods and programming, Tome 21 (2020) no. 2, pp. 138-151

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A software package for the mathematical simulation of thermo-poroelastic medium evolution with damage is considered. The employed model is a modification of the Biot model for thermo-poroelastic media and allows one to simulate the changes in the stress-strain state of the medium, the fluid flows, the nonisothermic effects, and the medium fracture. The medium damage is simulated using the continuum damage mechanics approaches by introducing a special variable called the damage parameter. This parameter characterizes the degree of medium fracture and its evolution is described by a given kinetic equation. The numerical algorithm is based on a finite element method. The time discretization is performed using an implicit scheme for displacements, pressure, and temperature and an explicit scheme for the damage parameter. The Taylor-Hood finite elements of second-order approximation in displacements and first-order approximation in pressure and temperature are chosen. The system of equations is solved in the framework of the “monolithic” formulation without the iterative coupling between groups of equations. The numerical results of solving the problem on the rock damage evolution due to thermal action are discussed.
Keywords: thermoporoelasticity; Biot model; fracture; thermodynamic consistency principle; finite element method. 
@article{VMP_2020_21_2_a1,
     author = {A. S. Meretin},
     title = {A software package for the mathematical simulation of fracture in a thermo-poroelastic medium},
     journal = {Numerical methods and programming},
     pages = {138--151},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_2_a1/}
}
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A. S. Meretin. A software package for the mathematical simulation of fracture in a thermo-poroelastic medium. Numerical methods and programming, Tome 21 (2020) no. 2, pp. 138-151. http://geodesic.mathdoc.fr/item/VMP_2020_21_2_a1/