We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. We establish existence and uniqueness of a solution to the weak formulation and its semidiscrete continuous-in-time finite element approximation. We present error analysis, complemented by numerical experiments.
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Second‐order time discretization for a coupled quasi‐Newtonian fluid‐poroelastic system
Numerical methods are proposed for the nonlinear Stokes‐Biot system modeling interaction of a free fluid with a poroelastic structure. We discuss time discretization and decoupling schemes that allow the fluid and the poroelastic structure computed independently using a common stress force along the interface. The coupled system of nonlinear Stokes and Biot is formulated as a least‐squares problem with constraints, where the objective functional measures violation of some interface conditions. The local constraints, the Stokes and Biot models, are discretized in time using second‐order schemes. Computational algorithms for the least‐squares problems are discussed and numerical results are provided to compare the accuracy and efficiency of the algorithms.
more » « less- Award ID(s):
- 1818842
- NSF-PAR ID:
- 10457737
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Fluids
- Volume:
- 92
- Issue:
- 7
- ISSN:
- 0271-2091
- Page Range / eLocation ID:
- p. 687-702
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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