(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
This work aims to provide guidance for selection between the implicit and explicit immersed boundary methods (IBMs). The implicit method ensures satisfaction of the boundary condition in one correction step (Wu and Shu, J. Comput. Phys., 228 (2009), pp. 1963–1979). However, it requires formation of a relatively complex matrix. The computational time of this method for moving boundary problems is also a concern, because matrix operations are required at each time step. On the other hand, the explicit multi-direct forcing (MDF) (Luo et al., Phys. Rev. E, 76 (2007), 066709) methods are more straightforward. Nevertheless, the detailed comparison between the two methods is lacked in the literature. In this work, the implicit method, the MDF method, MDF method with under/over-relaxation parameters are compared in detail through simulation of stationary and moving boundary problems. It is found that the implicit method generally outperforms the explicit methods, in respects of maintaining both accuracy and computational efficiency. The present study suggests that it can be worthy to form the matrix and solve the equation system implicitly in IBM for both stationary and moving boundary problems.