The penalty IB method which was introduced by
C.S.Peskin and myself is
a new and simple way to give mass to the elastic boundary within the IB framework.
The key idea is to introduce a massive boundary point as a twin of each immersed
boundary marker where mass is needed.
The two boundaries are supposed to be the same, and when they move
apart, a strong restoring force arises to pull them back together.
The massive boundary moves according to Newton's law without interacting
directly with the fluid, and the original immersed boundary
plays the same role as in the original IB method with no mass.
When there are two fluid with different densities interfacing each other,
we can use the pIB method to simulate the two fluid interaction in many different
situations.
