Sources of spurious force oscillations from an immersed boundary method for moving-body problems

When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132–150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.