A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder (Advances in Applied Mathematics and Mechanics, 2021)
A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM)is presented in this work. The present approach is an improvement to the conventionalIB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximatelysatisfied. As a result, there is flow penetration to the solid boundary. Another drawbackof conventional IB-LBM is the use of Dirac delta function interpolation, which only hasthe first order of accuracy. In this work, the no-slip boundary condition is directlyimplemented, and used to correct the velocity at two adjacent mesh points from bothsides of the boundary point. The velocity correction is made through the second-orderpolynomial interpolation rather than the first-order delta function interpolation.Obviously, the two drawbacks of conventional IB-LBM are removed in the present study.Another important contribution of this paper is to present a simple way to compute thehydrodynamic forces on the boundary from Newton's second law. To validate the proposedmethod, the two-dimensional vortex decaying problem and incompressible flow over acircular cylinder are simulated. As shown in the present results, the flow penetrationproblem is eliminated, and the obtained results compare very well with available datain the literature.