An embedded boundary method for an inviscid compressible flow coupled to deformable thin structures: The mediating body method

Abstract

This article deals with fast transient phenomena involving fluids and structures undergoing large displacements and rotations, associated with nonlinear local behavior, such as plasticity, damage, and failure. A new approach is proposed to handle the interaction between a structure and the compressible fluid it is immersed into. The equations governing the evolution of the structure and the fluid are discretized using Lagrangian shell finite-elements and Eulerian cell-centered finite volume approaches, respectively. The meshes of the structure and the fluid are totally independent from one another and fully unstructured. The proposed method uses an intermediate body through which the physical quantities are exchanged between the fluid and the structure. It relies on the solution of local one-dimensional fluid-structure Riemann problems in local frames related to the normal of the structure. Since the proposed approach does not require to subdivide the fluid cell according to the structure geometry, it can deal with complex nonmanifold thin structures. Nevertheless, it is shown through some numerical experiments that, thanks to some features described in this article, the method provides accurate results. It is also shown that the method can cope with large 3D problems. KEYWORDS compressible flow, embedded structures, finite element, finite volume, fluid-structure interaction, unstructured meshes INTRODUCTIONThis article deals with fast transient phenomena involving fluids and structures undergoing large displacements and rotations, associated with nonlinear local behavior, such as plasticity, damage, and failure. In this context, classical ALE approaches (for arbitrary Lagrangian Eulerian, see the works of Donea et al 1 or Hirt et al 2 ) reach a limit where it is not possible to update the fluid grid to follow the structural motion without encountering entangled fluid cells forcing the simulations to stop. Furthermore, even in the case of a motionless but complex structure, the conformity constraint between the fluid and structure meshes can make the construction of the fluid mesh a difficult task and lead to unwanted features of the resulting fluid mesh such as overrefined zones or low quality elements.Since the pioneering work of Peskin with the immersed boundary method, 3,4 several approaches allow to break the topological connection between the fluid and structural meshes and retrieve the expected level of robustness and flexibility to handle complex structural geometry and motions. One can think, for example, about the immersed interface Int J Numer Methods Eng. 2019;119:305-333.wileyonlinelibrary.com/journal/nme