Conservative load transfer along curved fluid-solid interface with non-matching meshes

We investigate the effect of curvature on the accuracy of schemes used to transfer loads along the interface in coupled fluid-solid simulations involving non-matching meshes. We analyze two types of load transfer schemes for the coupled system: (a) point-to-element projection schemes and (b) common-refinement schemes. The accuracy of these schemes over the curved interface is assessed with the aid of static and transient problems. We show that the point-to-element projection schemes may yield inaccurate load transfer from the source fluid mesh to the target solid mesh, leading to a weak instability in the form of spurious oscillations and overshoots in the interface solution. The common-refinement scheme resolves this problem by providing an accurate transfer of discrete interface conditions across non-matching meshes. We show theoretically that the accurate transfer preserves the stability of the coupled system while maintaining the energy conservation over a reference interface. Finally, we introduce simple analytical error functions which correlate well with the numerical errors of the load transfer schemes.