A vorticity based approach to handle the fluid-structure interaction problems

A vorticity based approach for the numerical solution of the fluid-structure interaction problems is introduced in which the fluid and structure(s) can be viewed as a continuum. Retrieving the vorticity field and recalculating a solenoidal velocity field, specially at the fluid-structure interface, are the kernel of the proposed algorithm. In the suggested method, a variety of constitutive equations as a function of left Cauchy–Green deformation tensor can be applied for modeling the structure domain. A nonlinear Mooney–Rivlin and Saint Venant–Kirchhoff model are expressed in terms of the left Cauchy–Green deformation tensor and the presented method is able to model the behavior of a visco-hyperelastic structure in the incompressible flow. Some numerical experiments, with considering the neo-Hookean model for structure domain, are executed and the results are validated via the available results from literature.