Sensitivity to the application range of buoyancy force in the diffuse-interface immersed boundary method

Abstract

We investigate the sensitivity to the application range of buoyancy force near the boundary in the diffuse-interface immersed boundary method. The flow fields not only inside the boundary but also outside the boundary are usually computed in the immersed boundary method. From a physical point of view, the buoyancy force should be zero inside the boundary and applied only outside the boundary. In addition, in diffuse-interface methods, the boundary is expressed by the volume force distributed near the boundary, i.e., there is an ambiguity in distinguishing the inside and outside of the boundary. In the present study, we define the application range of buoyancy force by using a weighting function which smoothly varies from 0 to 1 with a small thickness ξ, which expresses the ambiguity of the boundary. In order to investigate the effect of the application range of buoyancy force, we simulate the sedimentation of a cold circular cylinder in a heated channel, where the buoyancy force has a significant effect on the flow and temperature fields and the cylinder motion, for various values of ξ. As a result, we find that the results are very sensitive to the application range, and the movement pattern of the cylinder significantly varies depending on the value of ξ, even when it is less than one lattice spacing. Since each of the results with different values of ξ is supported by different existing studies, an appropriate value of ξ is unclear. These results pose a problem on an appropriate application range of buoyancy force in the diffuse-interface method, which has been overlooked.