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

Abstract

An immersed interface-lattice Boltzmann method (II-LBM) is developed for modeling 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 where forces are imposed along a surface immersed in an incompressible fluid. In this initial II-LBM, the discontinuity related to the normal component of the interfacial force is sharply resolved by imposing the relevant jump conditions using an approach that is analogous to imposing the corresponding pressure discontinuity 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). In our implementation, a level set approach is used to impose jump conditions for rigid-body models. For flexible boundary models, we describe the moving interface by interpolating the positions of marker points that move with the fluid. The II-LBM introduced herein is compared to a direct forcing IB-LBM for rigid-body fluid-structure interaction, and a classical IB-LBM for cases involving elastic interfaces. Higher order accuracy is observed with the II-LBM as compared to the IB-LBM for selected benchmark problems. Although our II-LBM only imposes jump conditions corresponding to the pressure, the error in the velocity field is demonstrated to be 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.