Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid–structure interaction problems

Abstract

SUMMARYEmbedded boundary methods for CFD (computational fluid dynamics) simplify a number of issues. These range from meshing the fluid domain, to designing and implementing Eulerian-based algorithms for fluidstructure applications featuring large structural motions and/or deformations. Unfortunately, embedded boundary methods also complicate other issues such as the treatment of the wall boundary conditions in general, and fluid-structure transmission conditions in particular. This paper focuses on this aspect of the problem in the context of compressible flows, the finite volume method for the fluid, and the finite element method for the structure. First, it presents a numerical method for treating simultaneously the fluid pressure and velocity conditions on static and dynamic embedded interfaces. This method is based on the exact solution of local, one-dimensional, fluid-structure Riemann problems. Next, it describes two consistent and conservative approaches for computing the flow-induced loads on rigid and flexible embedded structures. The first approach reconstructs the interfaces within the CFD solver. The second one represents them as zero level sets, and works instead with surrogate fluid/structure interfaces. For example, the surrogate interfaces obtained simply by joining contiguous segments of the boundary surfaces of the fluid control volumes that are the closest to the zero level sets are explored in this work. All numerical algorithms presented in this paper are applicable with any embedding CFD mesh, whether it is structured or unstructured. Their performance is illustrated by their application to the solution of three-dimensional fluid-structure interaction problems associated with the fields of aeronautics and underwater implosion.

FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps

“…This framework is suitable not only for multi-fluid applications, but also for multi-material flow problems involving static or dynamic, rigid or flexible solid domains. In particular, it is usually preferred over the Lagrangian and ALE frameworks [21][22][23] for the solution of high-speed compressible fluid-structure and multi-fluid-structure interaction problems characterized by large structural deformations [24][25][26] and/or topological changes such as those associated with crack propagation.…”

Multiphysics simulations: challenges and opportunities.

“…In this case, large mesh motions are handled by a corotational approach, which separates the rigid and deformational components of the motion of the surface of the obstacle (Farhat et al, 2001) and robust mesh motion algorithms that are based on structural analogies (Farhat et al, 1998a). In the case of embedded surfaces that can have complex shapes and arbitrary thicknesses, the governing equations of fluid motion are formulated in the Eulerian framework, and the wall boundary or transmission conditions are treated by an embedded boundary method (Wang et al, 2011a). Both AERO-F and AERO-S feature explicit and implicit time integrators with adaptive timestepping.…”

A Three-Dimensional Conservative Coupling Method Between an Inviscid Compressible Flow and a Moving Rigid Solid

“…In the military or safety domains, the effects of an explosion on a building or on a submarine involve complex non-linear phenomena (shock waves, cracking, rupture, ...) [28,30]. The characteristic time scale of these phenomena is extremely short and the driving effect of the interaction is the overpressure.…”