A hybrid Fourier continuation-lattice Boltzmann method for the numerical simulation of 3D incompressible fluid-structure interactions

This contribution proposes a new hybrid numerical approach for simulating 3D fluid-structure interactions, where solid structures (modeled as thin walls or shells) are resolved by a modified Fourier continuation (FC) method. Partial differential equation solvers based on such a method have demonstrated the ability to provide high-order accuracy while incurring minimal dispersion or pollution errors. This work, in particular, introduces a new set of continuation operators for treating the multiple conditions that can exist at shell boundaries in Lagrangian coordinate systems (e.g., simply-supported fixed ends). Together with a flow solver facilitated by a lattice Boltzmann method (LBM), the overall algorithm, which is based on structured grids, enables faithful capturing of the effects of high-frequency wave/vibration propagation through thin structures that are immersed in fluids. The complete fluid-structure numerical model is well-suited for patient-specific configurations in hemodynamics simulations. Convergence, error, and computational cost analyses are performed with both analytical and manufactured solutions. Realistic case studies are presented in order to demonstrate the applicability of the hybrid FC-LBM methodology.