arXiv:2611.06335v1 Announce Type: new Abstract: In this paper,we consider a stable numerical method for the Stokes-Biot model. We adopt the standard formulation of the Stokes equations coupled with the mixed formulation of the Biot system involving the additional total pressure variable. We construct the semi-discrete scheme on polygonal meshes by employing weak Galerkin finite element methods for spatial discretization. It is convenient to incorporate the interface conditions into the semi-discrete scheme via the edge-based degrees of freedom. Furthermore, we give a fully discrete scheme based on the backward Euler method. We establish the well-posedness of these two schemes and provide a rigorous error analysis. Finally, we present some numerical examples to verify the convergence and stability of our algorithm under a wide range of some physical parameters.