A cell boundary–element method is developed to solve viscous fluid–structure interaction problems modelled by Navier–Stokes equations. This is achieved through a hybrid approach incorporating boundary–element and finite–element methods. In the proposed scheme, cell equations are generated using the principles of the boundary–element method with global equations derived following the procedures of the finite–element method. A primitive–variable formulation with an unstructured mesh requirement forms the basis of the hybrid approach which can be applied to both two– and three–dimensional problems.
The validation of this numerical scheme of study involving analytical and numerical mathematical procedures is carried out using a number of well–documented flow solutions and the accuracy and robustness of the method are demonstrated in these examples.