Novel immersed boundary-lattice Boltzmann method based on feedback law

The lattice Boltzmann method (LBM) and the immersed boundary method (IBM) are alternative, computational techniques for solving complex fluid dynamics systems, and can take the place of the Navier-Stokes (N-S) equation. This paper proposes a novel immersed boundary-lattice Boltzmann method (IB-LBM) based on the feedback law. The method uses the immersed boundary concept in the LBM framework to capture the coupling between a body with complex geometry and a uniform fluid, Then, the flows around a stationary circular cylinder and two circular cylinders in a side by side arrangement are simulated by using the method. Results are agreed well with the benchmark data, so, the capability of the method for complex geometry is demonstrated. Different from the conventional IB-LBM, which uses the Hook's law or the direct forcing method to compute the interaction force, the method uses the feedback law-the feedback of velocity field and displacement information to calculate the force, thus ensuring the method has advantages of easy implementation and full parallelism.