Truncation error and energy conservation for fluid–structure interactions Original Research Article

his paper describes the numerical analysis of low speed large displacements fluid–structure interaction problems. After reviewing the basic conservation principles and kinematic interface conditions governing the problem under study, it concentrates on truncation error and kinetic energy conservation. Such properties are indeed crucial for checking both the stability and convergence of the numerical scheme and the physical stability of the mechanical system under study. We observe that classical time integration schemes which are dissipative, unconditionally stable and accurate for fluids flowing inside fixed domains may loose their long term stability properties when used on moving domains. We also produce new estimates proving that high order schemes using a partially nonconservative formulation associated to the variable ρJU properly conserve the kinetic energy, and that the same schemes used on different formulations only conserve this energy approximately, with an error which depends on the smoothness of the grid deformations and on the truncation error in the equation of mass conservation. Numerical results finally illustrate the approach.