Accuracy of the laminar boundary layer on a flat plate in an immersed boundary-lattice Boltzmann simulation

Abstract

We investigate the accuracy of the laminar boundary layer on a flat plate in the simulation by an immersed boundary-lattice Boltzmann method (IB-LBM). In this study, we use the single relaxation time-lattice Boltzmann method combined with the multi direct forcing method, which can enforce the no-slip boundary condition accurately by determining the body force iteratively. The simulations of the laminar boundary layer on a flat plate at the Reynolds number of 1000 are performed by using the IB-LBM, and it is found that in order to obtain a reasonably accurate result such that the error from the solution of the boundary layer equations is within 5%, the boundary layer has to be resolved by about 50 lattice spacings. In addition, it is found that the IB-LBM has the same accuracy whether the flat plate is coincident with the lattice or not. In order to improve the accuracy of the boundary layer calculated by the IB-LBM, we discuss the effective thickness of the boundary caused by the body force distributed near the boundary. Also, we find that the accuracy is much improved by using a finer lattice only around the flat plate.