Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics

• Published in: International journal for numerical and analytical methods in geomechanics 2015-10, Vol.39 (14), p.1593-1618
• Main Authors: Castelletto, N., White, J. A., Tchelepi, H. A.
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Approximation; Complement; Computational efficiency; finite element; GEOSCIENCES; iterative fixed-stress scheme; iterative fixed-stress scheme; Joining; Mathematical analysis; Mathematical models; multipoint flux approximation; multipoint flux approximation; poromechanics; Preconditioning; finite element
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.2400

Summary The paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite‐element and multipoint flux approximation finite‐volume methods. The solution algorithm relies on the recently developed fixed‐stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element‐wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well‐known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed‐stress scheme in accurately capturing the two‐way coupling between deformation and pressure. Copyright © 2015 John Wiley & Sons, Ltd.