Extended immersed boundary method using FEM and RKPM Original Research Article

The proposed extended immersed boundary method (EIBM) has several distinct features in comparison with the immersed boundary (IB) method. In the IB method, the interaction between the immersed elastic boundary and the surrounding viscous fluid is replaced with an equivalent body force distribution within the fluid domain. The key ingredient of the IB method is the enforcement of the energy input from the equivalent body force into the fluid domain to be the same (at all time) as that of the elastic forces within the IB. In EIBM, instead of the volumeless immersed elastic boundary, we consider the submerged elastic solid which occupies a finite volume within the fluid domain. In particular, we replace the kinematic and dynamic matching of the fluid–solid interface and the effect of the submerged solid with a judiciously chosen collection of equivalent nodal forces calculated in the context of finite element formulations. The employment of the finite element representation enables a realistic stress analysis for the submerged solid subject to large deformations. Finally, in EIBM, we also replace the discretized delta function commonly used in the IB method with the kernel functions in meshless reproducing kernel particle method (RKPM). With this improvement, using the same finite support domain, we could improve the discretized delta function from C1 to Cn continuity, where n is chosen according to the required smoothness and resolution of such functions, and more importantly, enables the use of non-uniform meshing in the fluid domain. These extensions may eventually open doors to the modelling of complex biological fluid involving molecular, cellular, and flexible vessel–flow interactions.