An Eulerian–Lagrangian–Lagrangian method for solving thin moving rigid body immersed in the fluid

Abstract

It is convention in computational mechanics to use Eulerian grids for fluids and Lagrangian grids for solids. In this paper, a novel method called ELL using both Lagrangian and Eulerian grids for fluids is presented in a carefully designed manner to handle complex fluid–structure interaction (FSI) problems with moving thin rigid body. The key idea is to use a small portion of the fluid to wrap the thin body. This wrapping fluid is described in Lagrangian coordinate, the same way the solid is described. They are treated as one “composite solid” thus the immersed domain method (IDM) can be implemented. In this way, the moving interface boundary conditions can be explicitly imposed with the help of the unified Lagrangian grids in the interaction zone. The initial fluid domain can still be treated as usual Eulerian grids based on IDM theory by introducing a fictitious fluid. The FSI interface can be accurately modeled since the wrapping fluid and the solid are always attached together. This effectively solves the major “blur interface” problem in the conventional immersed boundary method (IBM). To demonstrate this ELL idea, a number of benchmark examples have been studied in comparison with the results in the open literature. Finally, a 2D flapping wing is simulated to show the potential of ELL in engineering application. It is observed that ELL method proves to be good in performance.