AuthorsM. E. Rognes and T. Thompson
TitleA robust mixed finite element method for generalized poroelasticity
AfilliationScientific Computing
Project(s)Waterscape: The Numerical Waterscape of the Brain
Publication TypeTalks, invited
Year of Publication2018
Location of TalkGlasgow, UK
Type of TalkTechnical Talk: Numerical Analysis, Scientific Computing
Keywordsbrain mechanics, mixed finite element methods, multiple-network poroelasticity

The classical Biot and Terzaghi soil models, describing flow through a single fluid network in a porous and elastic medium, were generalized to equations describing multiple fluid network poroelasticity (MPET) by Barenblatt and Aifantis.  The MPET equations have been utilized in geomechanics to simulate multiple fractured strata for a few decades, but are now also beginning to find their application in biomechanics. Indeed, the multiple network poroelasticity theory aptly models the multiple fluid networks encountered in e.g. the brain: such as extracellular spaces, vasculature and paravasculature.  


In this talk, we propose a new mixed finite element formulation for the multiple-network poroelasticity equations. The key idea is to introduce the network fluid fluxes as additional variable targeting a finite element formulation that is robust with respect to low hydraulic conductivities and storage coefficients. We will present both theoretical and numerical results regarding the robustness and convergence of the new method, together with numerical demonstrations relating to the topic of cerebral interstitial and
paravascular fluid flow.

Citation Key25823

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