Eulerian finite volume method using Lagrangian markers with reference map for incompressible fluid-structure interaction problems

We propose a monolithic fluid-structure interaction (FSI) method that presents the advantages of both the reference map technique (RMT) and the Lagrangian Markers approach on a unified, cell-centered finite volume Eulerian framework. Full Eulerian methods that use a Cartesian mesh are attractive for FSI problems that require large-scale computing and involve complex geometries and large solid deformations. However, conventional full Eulerian methods use the velocity gradient to evaluate solid deformations, hence they suffer from numerical instability caused by the discontinuity of the velocity gradient near the interface. In this work, we develop a novel algorithm that interpolates and transfers a reference mapping information field between a collection of Lagrangian Markers and a Eulerian finite volume framework. As a result of integrating these approaches, our method is able to (1) evaluate solid deformations without computing the velocity gradient in the Eulerian framework thanks to RMT, and (2) remove the numerical dissipation of interfaces and internal variables caused by advection in the full Eulerian RMT, thanks to the use of the Lagrangian Markers to compute the constitutive equations. We illustrate with numerical examples that the proposed method preserves geometrical features and yields more accurate results for the deformation and energy than conventional Eulerian FSI method and the full Eulerian RMT.