Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

Abstract

An immersed boundary-lattice Boltzmann method (IB-LBM) using a two-relaxation time model (TRT) is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1) the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT) model causes a large non-physical velocity distortion at a high relaxation time, (2) the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3) the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4) the functional form of the direct-forcing term does not affect predictions, and (5) circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.