Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations

In this paper higher order time integration schemes are applied to structural dynamics and fluid-structure interaction (FSI) simulations. So far only second order accurate time integration schemes have been successfully applied to fluid-structure interaction simulations. For equal accuracy the higher order time integration schemes can require less computational work then a lower order method, leading to a higher computational efficiency. In the partitioned FSI simulations on a one-dimensional piston test problem, a mixed implicit/explicit (IMEX) time integration scheme is employed: the implicit scheme is used to integrate the fluid and structural dynamics, whereas an explicit Runge–Kutta scheme integrates the coupling terms. The resulting IMEX scheme retains the order of the implicit and explicit schemes. In the IMEX scheme considered, the implicit scheme consists of an explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) scheme, which is a multi-stage, L-stable scheme. Since, the ESDIRK scheme has not been previously applied to structural dynamics, it is used to integrate a number of simple structural dynamics problems to investigate the performance of the scheme. The ESDIRK scheme allows a direct and efficient integration of the cases considered.