A semi-decoupled MAC scheme for the coupled fluid-poroelastic material interaction

In this paper, a semi-decoupled marker and cell (MAC) scheme is proposed for the Stokes-Biot system, in which the displacement of structure is split from the whole system using the time-lagging scheme, then the rest system composed by the velocity and pressure is treated in a similar way as the Stokes-Darcy coupling problem. It keeps the desirable qualities such as the mass conservation. The backward Euler scheme is used for the time discretization. We derive the stability and the error estimates for the fully discrete scheme, obtain the second order superconvergence for the discrete L-2 norm for velocity, pressure and displacement and some terms of the H-1 norm for displacement and velocity. Numerical experiments confirm well the theoretical analysis results and the robustness of parameters.

Automated summary

In this paper, a semi-decoupled marker and cell (MAC) scheme is proposed for the Stokes-Biot system, which separates the displacement of the structure from the whole system using a time-lagging scheme. The remaining system composed of velocity and pressure is treated similarly to the Stokes-Darcy coupling problem. The scheme preserves desirable qualities such as mass conservation. The stability and error estimates for the fully discrete scheme are derived, showing second order superconvergence for the discrete L-2 norm of velocity, pressure, and displacement, as well as some terms of the H-1 norm for displacement and velocity. Numerical experiments confirm the theoretical analysis results and parameter robustness.