The immersed boundary-lattice Boltzmann method for solving solid-fluid interaction problem with Navier-slip boundary condition

Abstract

To solve the solid-fluid interaction with Navier-slip boundary condition, we propose a new method in this paper. In this approach, the solid body is modeled by the Newton’s equations and the fluid is assumed to satisfy the discrete lattice Boltzmann equations. The Navier-slip boundary condition is applied as the velocity boundary condition for the solid-fluid interface. We discretize the Newton’s equations by a prediction/correction approach and the discrete lattice Boltzmann equations by a second-order finite difference scheme in space together with a second-order Range–Kutta scheme in time. The Navier-slip boundary condition and the immersed boundary body force are almost implicitly updated by using the implicit velocity correction-based immersed boundary-lattice Boltzmann method. Numerical simulations are carried out to verify the new presented method.