A mixed finite element method for nearly incompressible multiple-network poroelasticity

Lee, Jeonghun J.; Piersanti, Eleonora; Mardal, Kent‐André; Rognes, Marie E.

doi:10.48550/arxiv.1804.07568

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“…We mention that the fixed-stress scheme can be also used for non-linear extensions of Biot's equations, see [26] for non-linear water compressibility and [29,30,31,32] for unsaturated flow and mechanics. In these cases, one combines a linearization technique, e.g.…”

Section: Introductionmentioning

confidence: 99%

On the optimization of the fixed‐stress splitting for Biot's equations

Storvik

Both

Kumar

et al. 2019

Numerical Meth Engineering

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Summary In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf‐sup stable with respect to the displacement‐pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme's optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations.

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