Numerical Solution of Thermoporoelasticity Problems
We consider the numerical solution of thermoporoelasticity problems. The basic system of equations includes the Lame equation for the displacement and two nonstationary equations for the fluid pressure and temperature. The computational algorithm is based on the finite element approximation in space and the finite difference approximation in time. We construct standard implicit scheme and unconditionally stable splitting schemes with respect to physical processes, when the transition to a new time level is associated with solving separate sub-problems for the desired displacement, pressure, and temperature. The stability of the scheme is achieved by passing to three-level difference scheme and by choosing a weight used as a regularization parameter. We provide the stability condition of the splitting scheme and present numerical experiments supporting this condition.
KeywordsBilinear Form Coarse Mesh Implicit Scheme Temperature Increment Finite Element Approximation
This research was supported by RFBR (project N14-01-00785A).
- 1.Alexsson, O., Blaheta, R., Byczanski, P.: Stable discretization of poroelastiicty problems and efficient preconditioners for arising saddle point type matrices. Comput. Vissualizat. Sci. 15(4), 191–2007 (2013)Google Scholar
- 10.Marchuk, G.I.: Splitting and alternating direction methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, I, North-Holland, pp. 197–462 (1990)Google Scholar