  This paper presents a novel stabilized mixed material point method (MPM)
designed for the unified modeling of free-surface and seepage flow. The unified
formulation integrates the Navier-Stokes equation with the
Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both
non-porous and porous domains. In contrast to the conventional Eulerian
computational fluid dynamics (CFD) solver, which solves the velocity and
pressure fields as unknown variables, the proposed method employs a monolithic
displacement-pressure formulation adopted from the mixed-form
updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup
stability condition, a stabilization strategy based on the variational
multiscale method (VMS) is derived and integrated into the proposed
formulation. Another distinctive feature is the implementation of blurred
interfaces, which facilitate a seamless and stable transition of flows between
free and porous domains, as well as across two distinct porous media. The
efficacy of the proposed formulation is verified and validated through several
benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples
demonstrate enhanced accuracy and stability compared to analytical,
experimental, and other numerical solutions.
