A new formulation for correcting the pressure field in Viscous Potential Theory (VPT) is developed, generalizing previous Viscous Pressure Correction (VPC) methods to simulate multi-phase flows based on VPT. The latter theory is now applicable to a wider range of flow problems. Without limiting the general applicability of the formulation, the present work focuses on the dynamics of two-dimensional liquid blobs and liquid films in a void. The governing equations of the method are solved using the traditional Boundary Element Method together with fourth-order Runge-Kutta time-integration, thereby reducing the spatial dimension of the problem by one and increasing the computational efficiency dramatically as compared to general purpose solvers for interfacial flows. Verification and Validation of the new method and algorithm are carried out through comparison of the simulation results with those obtained from (semi-)analytical models, a general-purpose OpenFOAM solver with Volume-of-Fluid interface treatment, and a Smoothed-Particle Hydrodynamics solver. Several benchmark cases and a wide range of viscosities are considered. Significantly improved accuracy of the newly proposed method as compared to the original Viscous Pressure Correction of Viscous Potential Flow (VCVPF) approach is demonstrated for the case of a retracting free liquid film or ligament. In order to demonstrate the capacity of the present method and algorithm in handling complex multiphase flow problems and in providing physical insight into such phenomena, the disintegration mechanism of a strongly modulated discharging liquid sheet under the influence of gravity is analyzed.

开发了一种新的公式来修正黏性势能理论（VPT）中的压力场，该模型概括了以前的黏性压力修正（VPC）方法，以基于VPT来模拟多相流。后一种理论现在适用于更广泛的流动问题。在不限制该制剂的一般适用性的情况下，本发明着重于二维液体团和液体膜在空隙中的动力学。与传统的界面求解器相比，使用传统的边界元方法和四阶Runge-Kutta时间积分来求解该方法的控制方程，从而将问题的空间维数减小了一个，并显着提高了计算效率流。通过将仿真结果与从（半）分析模型获得的仿真结果进行比较，新的方法和算法进行验证和验证，该仿真模型是从（半）分析模型，具有流体体积接口处理的通用OpenFOAM求解器和平滑粒子流体动力学中获得的解算器。考虑了几种基准情况和各种粘度。与回缩的自由液膜或韧带的情况相比，新提出的方法与原始的粘性势流的粘性压力校正（VCVPF）方法相比，显着提高了精度。为了证明本方法和算法在处理复杂的多相流问题以及提供对此类现象的物理见解方面的能力，