A higher-order immersed boundary-lattice Boltzmann method using a smooth velocity field near boundaries

Abstract

We propose a lattice Boltzmann method combined with a higher-order immersed boundary method using a smooth velocity field near boundaries. In usual immersed boundary methods, the body forces, which are applied only near the boundary in order to enforce the no-slip condition on the boundary, make a discontinuity of the velocity gradient on the boundary. This discontinuity makes the accuracy of flow computations only first-order in space. In order to avoid the discontinuity of the velocity gradient on the boundary, we propose a higher-order immersed boundary method for smoothly expanding the velocity field into the body domain across the boundary. The simulations of flows between two concentric cylinders show that this method achieves better than the first-order spacial accuracy both in maximum and mean error norms. In addition, we confirm that with the present method the force and the torque acting on the body can be obtained more accurately in the simulations of the flow around an oscillating circular cylinder and of the sedimentation of a sphere.