Combined interface boundary condition method for unsteady fluid–structure interaction

Traditionally, continuity of velocity and traction along interfaces are satisfied through algebraic interface conditions applied in a sequential or staggered fashion. In existing staggered procedures, the numerical treatment of the interface conditions can undermine the stability and accuracy of coupled fluid–structure simulations. This paper presents a new loosely-coupled partitioned procedure for modeling fluid–structure interaction called combined interface boundary condition (CIBC). The procedure relies on a higher-order treatment for improved accuracy and stability of fluid–structure coupling. By utilizing the CIBC technique on the velocity and momentum flux boundary conditions, a staggered coupling procedure can be constructed with similar order of accuracy and stability of standalone computations for either the fluids or structures. The new formulation involves a coupling parameter that adjusts the amount of interfacial traction in the form of acceleration correction, which plays a key role in the stability and accuracy of the coupled simulations. Introduced correction terms for velocity and traction transfer are explicitly added to the standard staggered time-stepping stencils based on the discretized coupling effects. The coupling scheme is demonstrated in the classical 1D closed- and open-domain elastic piston problems, but further work is needed to consider the analytical stability of these schemes, 3D problems and comparison to monolithic integration.