A Comparative Study of Interface Schemes in the Immersed Boundary Method for a Moving Solid Boundary Problem Using the Lattice Boltzmann Method

Abstract

For moving boundary problems, previous body-conformal grid methods require frequent re-meshing as the boundary moves, thus increasing computational cost. An immersed boundary method (IBM) is an attractive method to resolve the problem since it is based on the fixed, non-body-conformal grids. In the IBM, force density terms are used so that no-slip boundary condition is satisfied on the boundary. On the other hand, lattice Boltzmann methods (LBMs) have been used as an alternative of Navier-Stokes equation method due to their efficiency to parallelize and simplicity to implement. The common feature of the IBM and the LBM of using non-body-conformal grids motivated the use of the IBM in the lattice Boltzmann method frame, which is usually called an immersed boundary-lattice Boltzmann method (IB-LBM). Besides, a split-forcing property in the LBM, due to its kinetic nature, facilitates the use of direct-forcing IBM. For the evaluation of boundary force density term, we need to adopt an interpolation scheme because the boundary, in general, does not match computational nodes. The interpolation schemes can be classified into diffuse and sharp interface schemes. The former usually uses the discrete delta function to evaluate the boundary force on the prescribed boundary points, while the latter uses interpolation from neighboring fluid nodes to evaluate the boundary force on the computation node either inside or outside closest to the boundary. In the diffuse scheme, the boundary force density terms evaluated on the boundary points should be distributed onto neighboring computational nodes using the discrete delta functions so that the boundary effect may exert on computational process. The objective of this study is to compare two interface schemes simultaneously for a moving boundary problem under the IB-LBM and to understand advantages and disadvantages of each scheme. We considered a problem of flow induced by inline oscillation of a circular cylinder since both experimental and body-conformal grid method results are available for this problem. Velocity results from both schemes showed overall good agreement with experimental data. However, the sharp interface scheme showed spurious oscillations in the surface force coefficient and pressure fields, although after filtering or smoothing, the force coefficients showed good agreement with the body-fitted results. In contrast, the diffuse interface scheme produced smooth variations in the surface force coefficient but over-predicted the absolute values especially at phase angles with the high magnitude of accelerations. These results can be attributed to the use of discrete delta functions. We could reduce the over-prediction by considering the effect of the diffuse area.