An immersed interface-lattice Boltzmann method for fluid-structure interaction

Abstract: An immersed interface-lattice Boltzmann method (II-LBM) is developed for modelling fluid-structure systems. The key element of this approach is the determination of the jump conditions that are satisfied by the distribution functions within the framework of the lattice Boltzmann method when forces are imposed along a surface immersed in an incompressible fluid. In this initial II-LBM, the discontinuity related to the normal portion of the interfacial force is sharply resolved by imposing the relevant jump conditions using an approach that is analogous to imposing the corresponding pressure jump condition in the incompressible Navier-Stokes equations. We show that the jump conditions for the distribution functions are the same in both single-relaxation-time and multi-relaxation-time LBM formulations. Tangential forces are treated using the immersed boundary-lattice Boltzmann method (IB-LBM). The performance of the II-LBM method is compared to both the direct forcing IB-LBM for rigid-body fluid-structure interaction, and the classical IB-LBM for elastic interfaces. Higher order accuracy is observed with the II-LBM as compared to the IB-LBM for selected benchmark problems. Because the jump conditions of the distribution function also satisfy the continuity of the velocity field across the interface, the error in the velocity field is much smaller for the II-LBM than the IB-LBM. The II-LBM is also demonstrated to provide superior volume conservation when simulating flexible boundaries.