A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM)
is presented in this work. The present approach is an improvement to the conventional
IB-LBM. In the conventional IB-LBM, the no-slip boundary condition is only approximately
satisfied. As a result, there is flow penetration to the solid boundary. Another drawback
of conventional IB-LBM is the use of Dirac delta function interpolation, which only has
the first order of accuracy. In this work, the no-slip boundary condition is directly
implemented, and used to correct the velocity at two adjacent mesh points from both
sides of the boundary point. The velocity correction is made through the second-order
polynomial 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 the
hydrodynamic forces on the boundary from Newton's second law. To validate the proposed
method, the two-dimensional vortex decaying problem and incompressible flow over a
circular cylinder are simulated. As shown in the present results, the flow penetration
problem is eliminated, and the obtained results compare very well with available data
in the literature.