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Draft: Linear poroelastic model

Rezgar Shakeri requested to merge rezgar/poroelastic into main

Summary

This MR adds linear poroelasticity model. We need to solve

\int \nabla \bm v : \bm \sigma dV - \int \bm v \cdot \bm F dV - \int_{\partial \Omega} \bm v \cdot \bar{\bm t} \, dA = 0

where \bm F, \bar{\bm t} are body force and traction applied on porous medium and second equation

\int q \left( \dot{p}/M + \alpha \nabla \cdot \dot{\bm u} - \gamma \right) dV + \int \nabla q \left(\frac{k}{\eta} (\nabla p - \bm f) \right) dV + \int_{\partial \Omega} q  \bar{s} \, dA = 0

where \alpha, M are Biot's coefficient and Biot's modulus, k, \eta are intrinsic permeability and fluid viscosity and \gamma, \bm f are injected volumetric fluid source and fluid body force and \bar s = \bm v^D \cdot \bm n is the prescribed fluid flux across boundary in which \bm v^D is the Darcy's velocity.

Checklist

Closes #my_issue_number

  • Atomic commit history
  • All new features documented
  • Updated CHANGELOG.md
Edited by Rezgar Shakeri

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