A comparative study of immersed-boundary and interpolated bounce-back methods in LBE

The Interpolated Bounce-Back (IBB) method and Immersed-Boundary (IB) method are compared for fluid-solid boundary conditions in the Lattice Boltzmann Equation (LBE) in terms of their numerical accuracy and computational efficiency. We carry out simulations for the flow past a circular cylinder asymmetrically placed in the channel in two dimensions with the Reynolds number Re = 20 and 100, corresponding to steady and unsteady flows, respectively. The results obtained by the LBE method are compared with the existing data. We observe that the LBE with either the IBB or IB methods for the no-slip boundary conditions exhibits a second-order rate of convergence. While the computational cost for both methods are comparable, the interpolated bounce-back method is more accurate than the immersed-boundary method with the same mesh size. Consequently the IBB method is more efficient computationally, while the IB method is easier to implement.