Iterative splitting schemes for a soft material poromechanics model

• Published in: Computer methods in applied mechanics and engineering Vol. 388; p. 114183
• Main Authors: Both, J.W., Barnafi, N.A., Radu, F.A., Zunino, P., Quarteroni, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2022; Elsevier BV
• Subjects: Convergence analysis; Fixed-stress split; Gradient flow; Iterative methods; Iterative splitting schemes; Mass balance; Poromechanics of soft materials; Robustness (mathematics); Solvers; Splitting; Stability analysis; Undrained split; Iterative splitting schemes; Poromechanics of soft materials; Undrained split; Fixed-stress split; Convergence analysis
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114183

We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid and fluid species, interacting on the basis of mass balance and momentum conservation, we decide to adopt a solution strategy of the discrete problem based on iterative splitting schemes. As the model is similar (but not equivalent to) the Biot poromechanics problem, we follow the abundant literature for solvers of the latter equations, developing two approaches that resemble the well known undrained and fixed-stress splits for the Biot model. A thorough convergence analysis of the proposed schemes is performed. In particular, the undrained-like split is developed and analyzed in the framework of generalized gradient flows, whereas the fixed-stress-like split is understood as block-diagonal L2-type stabilization and analyzed by means of a relative stability analysis. In addition, the application of Anderson acceleration is suggested, improving the robustness of the split schemes. Finally, we test these methods on different benchmark tests, and we also compare their performance with respect to a monolithic approach. Together with the theoretical analysis, the numerical examples provide guidelines to appropriately choose what split scheme shall be used to address realistic applications of the soft material poromechanics model. •Two iterative block-partitioned solvers are proposed for a poromechanics model addressing flow in soft tissues.•Theoretical convergence is established for both methods with rates independent of the mesh size.•Extensive numerical tests verify the theory and enable a direct comparison of both methods.•Anderson acceleration is suggested allowing for improved convergence behavior in practice.•A numerical comparison demonstrates potential gain of the proposed solvers for large problems, opposed to a monolithic solution.