  In this paper we show and discuss the use of a versatile interaction
potential approach coupled with an immersed boundary method to simulate a
variety of flows involving deformable bodies. In particular, we focus on two
kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii)
flow in the left ventricle of the heart with either a mechanical or a natural
valve. Both examples have in common the two-way interaction of the flow with a
deformable interface or a membrane. The interaction potential approach (de
Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura,
Computational Biomechanics, 2016) with minor modifications can be used to
capture the deformation dynamics in both classes of problems. We show that the
approach can be used to replicate the deformation dynamics of liquid-liquid
interfaces through the use of ad-hoc elastic constants. The results from our
simulations agree very well with previous studies on the deformation of drops
in standard flow configurations such as deforming drop in a shear flow or a
cross flow. We show that the same potential approach can also be used to study
the flow in the left ventricle of the heart. The flow imposed into the
ventricle interacts dynamically with the mitral valve (mechanical or natural)
and the ventricle which are simulated using the same model. Results from these
simulations are compared with ad- hoc in-house experimental measurements.
Finally, a parallelisation scheme is presented, as parallelisation is
unavoidable when studying large scale problems involving several thousands of
simultaneously deforming bodies on hundreds of distributed memory computing
processors.
