A grad-div stabilized penalty projection algorithm for fluid-fluid interaction

Abstract

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.