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.

翻译：本文提出一种新型稳定化混合物质点法（MPM），用于自由表面流与渗流的统一建模。该统一公式将纳维-斯托克斯方程与达西-布林克曼-福希海默方程相结合，有效捕捉非多孔域与多孔域中的流动特性。与求解速度场和压力场作为未知变量的传统欧拉计算流体动力学（CFD）求解器不同，所提方法采用从混合形式更新拉格朗日有限元法（FEM）引入的单片位移-压力公式。为满足离散inf-sup稳定性条件，基于变分多尺度方法（VMS）推导并集成了稳定化策略。另一独特特征在于采用模糊界面，该界面可实现自由域与多孔域之间以及两种不同多孔介质之间流动的无缝稳定过渡。通过一维、二维和三维场景下的多个基准算例，对所提公式的有效性进行了验证与确认。数值实验结果表明，与解析解、实验及其他数值解相比，本方法在精度和稳定性方面均有提升。