A subcycling/non-subcycling time advancement scheme-based DLM immersed boundary method framework for solving single and multiphase fluid–structure interaction problems on dynamically adaptive grids

In this paper, we present an adaptive implementation of the distributed Lagrange multiplier (DLM) immersed boundary (IB) method on multilevel collocated grids for solving single- and multiphase fluid–structure interaction (FSI) problems. Both a non-subcycling time advancement scheme and a subcycling time advancement scheme, which are applied to time-march the composite grid variables on a level-by-level basis, are presented; these schemes use the same time step size and a different time step size, respectively, on different levels. This is in contrast to the existing adaptive versions of the IB method in the literature, in which coarse- and fine-level variables are simultaneously solved and advanced in a coupled fashion. A force-averaging technique and a series of synchronization operations are constructed to achieve excellent momentum and mass conservation across multiple levels of grid hierarchy. We demonstrate the versatility of the present multilevel framework by simulating problems with various types of kinematic constraints imposed by structures on fluids, such as imposing a prescribed motion, free motion, and time-evolving shape of a solid body. The DLM method is also coupled to a robust level set method-based two-phase fluid solver to simulate challenging multiphase flow problems, including wave energy harvesting using a mechanical oscillator. The capabilities and robustness of the computational framework are validated against a variety of benchmarking single-phase and multiphase FSI problems from the literature, which include a three-dimensional swimming eel model to demonstrate the significant speedup and efficiency that result from employing the present multilevel subcycling FSI scheme.