A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane

Abstract

Jump conditions for the pressure, the velocity, and their normal derivatives across an immersed moving membrane in an incompressible fluid are derived. The discontinuities are due to the singular forces along the membrane. Instead of using the delta function formulation, those jump conditions can be used to formulate the governing equations in an alternative form. It is also useful for developing more accurate numerical methods such as immersed interface method for the Navier-Stokes equations involving moving interface.