In this paper, a new scheme is proposed to solve the Stokes interface problem. The scheme turns the Stokes interface problem into two coupled Stokes non-interface subproblems and adds a mixed boundary condition to overcome the numerical pressure oscillation. Since the interface becomes the boundary of the subproblems, the scheme has the advantage to deal with the interface problem with complex geometry. Furthermore, a generalized finite difference method (GFDM) is adopted to solve the coupled Stokes non-interface subproblems. The GFDM is developed from the Taylor series expansions and moving-least squares approximation. Due to the flexibility of the GFDM, it is convenient to handle the complex boundary conditions that appeared in the proposed scheme. The numerical examples verify the accuracy and stability of the GFDM to solve the Stokes interface problem with the mixed boundary conditions. Moreover, for some given numerical examples, the proposed scheme is more accurate than the classical formula of the pressure Poisson equation, especially in terms of pressure.

本文提出了一种解决Stokes接口问题的新方案。该方案将 Stokes 接口问题转化为两个耦合的 Stokes 非接口子问题，并添加混合边界条件来克服数值压力振荡。由于界面成为子问题的边界，因此该方案在处理具有复杂几何形状的界面问题时具有优势。此外，采用广义有限差分法（GFDM）求解耦合斯托克斯非接口子问题。GFDM 是从泰勒级数展开和移动最小二乘近似发展而来的。由于 GFDM 的灵活性，可以方便地处理所提出方案中出现的复杂边界条件。数值算例验证了GFDM求解混合边界条件下Stokes接口问题的准确性和稳定性。此外，对于一些给定的数值例子，所提出的方案比压力泊松方程的经典公式更准确，特别是在压力方面。