A one-field monolithic fictitious domain method for fluid-structure interactions

In this article, we present a one-field monolithic fictitious domain (FD) method for simulation of general fluid-structure interactions (FSI). “One-field” means only one velocity field is solved in the whole domain, based upon the use of an appropriate L2 projection. “Monolithic” means the fluid and solid equations are solved synchronously (rather than sequentially). We argue that the proposed method has the same generality and robustness as FD methods with distributed Lagrange multiplier (DLM) but is significantly more computationally efficient (because of one-field) whilst being very straightforward to implement. The method is described in detail, followed by the presentation of multiple computational examples in order to validate it across a wide range of fluid and solid parameters and interactions.