Eulerian finite volume formulation using Lagrangian marker particles for incompressible fluid-structure interaction problems

We propose a monolithic fluid-structure interaction (FSI) method that uses the cell-centered finite volume formulation in the Eulerian description, Lagrangian marker particles allocated in the solid region, and the incompressible mixture formulation. In the proposed method, we compute all the basic equations and spatial derivatives, except the solid constitutive equations, on an Eulerian mesh to avoid neighboring particle search. Although full Eulerian methods that use a Cartesian mesh are attractive for FSI problems that require large-scale computing and include complex geometries and the large deformation of the solid, they cannot avoid the numerical dissipation of the interfaces or internal variables of the solid caused by their advection. This computational problem has been a barrier to the industrial application of full Eulerian mesh methods. In the numerical examples, we confirmed that the proposed method retains sharp interfaces, such as the corners of a square solid, and yields more accurate numerical results for the deformation, energy, and incompressibility of a solid in fluid than our conventional Eulerian FSI method.