Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

Abstract

International audienceThis paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluid-structure interaction with complex geometry. First, a new stabilized three-field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the Navier-Stokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluid-solid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time-dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight

A new body-fitted immersed volume method for the modeling of ductile fracture at the microscale: Analysis of void clusters and stress state effects on coalescence

“…However, in these cases the deformation of the solid phase is usually neglected as the focus is made on the flow or on thermal exchanges. Hence, the authors impose the [18][19][20]. In these works, the interfaces are said to be implicit, as they are not carried by the mesh but only by the LS function.…”

“…That is the reason why a new mesh adaptation framework was developed. The parallel C++ library CimLib, which is used for the present developments, has already been used by multiple authors for simulations based on the LS method [14,15,[18][19][20][21][22]26]. For remeshing operations, the external C (re)mesher MTC was used [16].…”

“…This tool was extended to anisotropic mesh adaptation, for which it was extensively used [14,15,[18][19][20][21][22]26].…”

An anisotropic adaptive finite element algorithm for transonic viscous flows around a wing

“…The use of strongly anisotropic meshes involves several theoretical and practical issues: design of stable discretization methods [1], error estimates involving constants which do not depend on the mesh aspect ratio [2][3][4][5][6], convergence of solvers [7], generation of anisotropic meshes [8][9][10][11]. The possible gain in memory and computing time is so important that previously intractable problems may become tractable [12].…”

A three‐field stabilized finite element method for fluid‐structure interaction: elastic solid and rigid body limit

“…The level-set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid-solid interface.In this paper, we propose a new monolithic formulation where the complete problem is written in a fully Eulerian framework and the fluid and solid phases are separated by a level set function. The same approach was proposed in [10,11]. However, only the interactions between the fluid and rigid bodies were addressed, and therefore, the present paper is an extension of this previous work to allow dealing with elastic bodies, accounting for their full dynamics.…”