Theoretical considerations of the volume penalization immersed boundary method for turbulent flows

This Letter explores the volume penalization immersed boundary method for turbulent flows from a more physical perspective. The volume penalization approach consists of introducing a penalty source into the governing equations, resulting in a flow akin to a porous medium with low permeability. Although penalizing the turbulent equations conventionally involves adding a similar penalty source as in the original equations, this work reveals an alternative formulation that includes an additional term with physical meaning. The novelty of this Letter is to consider the penalized flow with an additional property, the fluid resistance, establishing a cross correlation with fluctuating velocity for further modeling.