A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss how the deformation dynamics of closed liquid-liquid interfaces (for example drops and bubbles) can be replicated with use of a phenomenological interaction potential model. This new approach to simulate liquid-liquid interfaces is based on the fundamental principle of minimum potential energy where the total potential energy depends on the extent of deformation of a spring network distributed on the surface of the immersed drop or bubble. Simulating liquid-liquid interfaces using this model require computing ad-hoc elastic constants which is done through a reverse-engineered approach. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as a deforming drop in a shear flow or cross flow. The interaction potential model is highly versatile, computationally efficient and can be easily incorporated into generic single phase fluid solvers to also simulate complex fluid-structure interaction problems. This is shown by simulating flow in the left ventricle of the heart with mechanical and natural mitral valves where the imposed flow, motion of ventricle and valves dynamically govern the behaviour of each other. Results from these simulations are compared with ad-hoc in-house experimental measurements. Finally, we present a simple and easy to implement parallelisation scheme, as high performance computing is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies in highly turbulent flows.