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A stabilized finite element method for finite-strain three-field poroelasticity
Lorenz Berger1, Rafel Bordas2, David Kay3
1Innersight Labs, 7 Astbury House, Lambeth Walk, London, SE11 6LZ UK.
Computational Mechanics
|February 7, 2020
Summary
We developed a stabilized finite-element method for incompressible poroelasticity, accurately simulating fluid flow and large deformations. This robust computational approach handles varying permeability and steep gradients effectively.
Area of Science:
- Computational mechanics
- Geophysics
- Biophysics
Background:
- Poroelasticity involves coupled fluid flow and solid deformation.
- Simulating finite-strain deformations in porous media presents computational challenges.
- Accurate modeling is crucial for geophysical and biological applications.
Purpose of the Study:
- To develop a stabilized finite-element method for incompressible poroelasticity.
- To directly compute displacement, fluid flux, and pressure.
- To ensure stability across a range of permeability values.
Main Methods:
- A three-field mixed finite-element formulation was employed.
- Low-order approximations (piecewise-linear for displacement/flux, piecewise-constant for pressure) were used.
- A Lagrange multiplier enforced flux boundary conditions.
Main Results:
- The method achieves stability for both small and large permeability.
- A simple matrix structure with low bandwidth was obtained.
- Discontinuous pressure spaces efficiently approximate steep gradients.
Conclusions:
- The developed method is a stable and efficient tool for simulating incompressible poroelasticity.
- It accurately captures complex phenomena like steep gradients in physical and biological systems.
- The low-order approximation simplifies the computational structure.
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