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.