The penalty projection algorithm (PP), which decouples pressure from the momentum equation of incompressible Navier–Stokes Equation (NSE), is among the most conventional approaches to simulate fluid flows. In a fluid-fluid decoupling setting, however, PP has never been employed but offers the potential for being one of the most typical candidates to compute two NSE’s in each subdomain. Although pressure decoupling weakens the divergence constraint, the proposed algorithm operates with a well-known grad-div stabilization technique to retrieve this property. Theoretical and computational findings demonstrate how the proposed grad-div stabilized PP method settles concerns and outperforms when implemented with fluid-fluid decoupling.

惩罚投影算法 (PP) 将压力与不可压缩纳维-斯托克斯方程 (NSE) 的动量方程解耦，是模拟流体流动的最传统方法之一。然而，在流体-流体解耦设置中，PP 从未被使用过，但它提供了成为计算每个子域中两个 NSE 的最典型候选者之一的潜力。尽管压力解耦削弱了发散约束，但所提出的算法使用众所周知的 grad-div 稳定技术来检索此属性。理论和计算结果证明了所提出的 grad-div 稳定 PP 方法如何解决问题并在使用流体-流体解耦实施时表现出色。