Comparative Study of Implicit and Explicit Immersed Boundary-Lattice Boltzmann Methods for Simulation of Fluid-Structure Interactions (Advances in Applied Mathematics and Mechanics, 2018)
This work aims to provide guidance for selection between the implicit andexplicit immersed boundary methods (IBMs). The implicit method ensures satisfactionof 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 complexmatrix. The computational time of this method for moving boundary problems is alsoa 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 betweenthe two methods is lacked in the literature. In this work, the implicit method, the MDFmethod, MDF method with under/over-relaxation parameters are compared in detailthrough simulation of stationary and moving boundary problems. It is found that theimplicit method generally outperforms the explicit methods, in respects of maintainingboth accuracy and computational efficiency. The present study suggests that it can beworthy to form the matrix and solve the equation system implicitly in IBM for bothstationary and moving boundary problems.