Fluid–structure interaction problems and multiphysics problems in general are often too complex to solve analytically and so they have to be analyzed by means of experiments or numerical simulation. Research in the fields of computational fluid dynamics and computational structural dynamics is still ongoing but the maturity of these fields enables numerical simulation of fluid-structure interaction. Two main approaches exist for the simulation of fluid–structure interaction problems:
*Monolithic approach: the equations governing the flow and the displacement of the structure are solved simultaneously, with a single solver
*Partitioned approach: the equations governing the flow and the displacement of the structure are solved separately, with two distinct solvers
The monolithic approach requires a code developed for this particular combination of physical problems whereas the partitioned approach preserves software modularity because an existing flow solver and structural solver are coupled. Moreover, the partitioned approach facilitates solution of the flow equations and the structural equations with different, possibly more efficient techniques which have been developed specifically for either flow equations or structural equations. On the other hand, development of stable and accurate coupling algorithm is required in partitioned simulations. In conclusion, the partitioned approach allows reusing existing software which is an attractive advantage. However, stability of the coupling method needs to be taken into consideration. This is especially difficult, if the mass of the moving structure is small in comparison to the mass of fluid which is displaced by the structure movement. 
In addition, the treatment of meshes introduces other classifications of FSI analysis. For example，one can classify them as the conforming mesh methods and the non-conforming mesh methods. Other classifications can be mesh-based methods and meshless methods.