Numerical investigation on the fixed-stress splitting scheme for Biot’s equations: optimality of the tuning parameter. (English) Zbl 1425.76132
Radu, Florin Adrian (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2017. Selected papers based on the presentations at the European conference, Bergen, Norway, September 25–29, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 126, 789-797 (2018).
Summary: We study the numerical solution of the quasi-static linear Biot equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We investigate numerically the optimality of the parameter and compare our results with physically and mathematically motivated values from the literature, which commonly only depend on mechanical material parameters. We demonstrate, that the optimal value of the tuning parameter is also affected by the boundary conditions and material parameters associated to the fluid flow problem suggesting the need for the integration of those in further mathematical analyses optimizing the tuning parameter.
For the entire collection see [Zbl 1411.65009].
For the entire collection see [Zbl 1411.65009].
MSC:
76M10 | Finite element methods applied to problems in fluid mechanics |
76M20 | Finite difference methods applied to problems in fluid mechanics |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65F10 | Iterative numerical methods for linear systems |
74S05 | Finite element methods applied to problems in solid mechanics |
76S05 | Flows in porous media; filtration; seepage |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
74E05 | Inhomogeneity in solid mechanics |
74B05 | Classical linear elasticity |