A stabilized Nitsche cut finite element method for the Oseen problem

Wall

2019

Summary Cut finite element method–based approaches toward challenging fluid‐structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed grid) and established arbitrary Lagrangian‐Eulerian (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving‐domain problems and to demonstrate their high potential with regard to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase, and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed‐grid FSI method, advanced fluid‐domain decomposition techniques are also considered, leading to highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche‐based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various two‐ and three‐dimensional FSI cases of different complexity levels validate the methods and demonstrate their capabilities and limitations in different situations.

Section: Finite Element Formulations—different Spatial Discretizationsmentioning

confidence: 99%

Monolithic cut finite element–based approaches for fluid‐structure interaction

Wall

2019

“…A comparison of different stabilization techniques for incompressible flow problems is presented in the work of Braack et al Face‐oriented stabilizations were applied for all numerical examples presented in Section 6. Details on the effectively applied formulations are given in the works of Massing et al for

{scriptW}_{scriptS}^{F}

and Ager et al for

{scriptW}_{scriptS}^{P}

.…”

Section: Discretization and Solution Approachmentioning

confidence: 99%

“…This so‐called “ghost penalty” stabilization was first presented in the work of Burman for the Poisson's problem. Details on the “ghost penalty” stabilization for the fluid equation, describing the applied method, can be found in the work of Massing et al Herein, operators are added, which penalize jumps of normal derivatives of velocities and pressures integrated on a selected set of element faces

{scriptF}_{{normalΓ}^{F, *}}

(see Figure ).

{scriptW}_{scriptG}^{F} ([], ((), δ {\underline{bold-italicv}}^{F}, δ p^{F}), ((), {\underline{bold-italicv}}^{F}, p^{F})) = {scriptG}_{v} ((), δ {\underline{bold-italicv}}^{F}, {\underline{bold-italicv}}^{F}) + {scriptG}_{p} ((), δ p^{F}, p^{F})

…”

Section: Discretization and Solution Approachmentioning

confidence: 99%

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

Vuong

et al. 2019

Summary Simulation approaches for fluid‐structure‐contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are 2‐fold—one is to have a correct physical model for this scenario, and the other is to have a numerical method that is capable of working and being consistent down to a zero gap. Moreover, when analyzing such challenging setups of fluid‐structure interaction, which include contact of submersed solid components, it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model that is able to include the effects of the surface microstructure in a fluid‐structure‐contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid are included in the construction of the model. Although the physical model is not restricted to finite element–based methods, a numerical approach with its core based on the cut finite element method, enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a cut finite element method–based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective toward the potential capabilities of the presented physical model and numerical approach.

“…Remark Due to the intersection of elements

T \in {scriptT}_{h}^{{normalf}_{1}}

by the fluid‐fluid interface

{normalΓ}^{{normalf}_{1} {normalf}_{2}}

, additional stabilization measures are required. Ghost‐penalty stabilizations

{scriptG}_{h}^{GP}

, as developed in the works of Schott and Wall and Massing et al, penalize jumps of normal derivatives of order j across interior facets F in the vicinity of the interface and thus ensure well system conditioning, stability, and optimality of the approximation independent of the mesh intersection. For further details on this technique, the reader is referred to, eg, other works …”

Section: A Cutfem‐based Hybrid Fsi Formulationmentioning

confidence: 99%

“…In the latter publication, even the use of different mesh sizes for background and wrapper mesh is discussed in detail. Further theoretical details can be found in related publications …”

Section: A Cutfem‐based Hybrid Fsi Formulationmentioning

confidence: 99%

A monolithic approach to fluid‐structure interaction based on a hybrid Eulerian‐ALE fluid domain decomposition involving cut elements

Wall

2019

Self Cite

Summary A novel method for complex fluid‐structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed‐grid) and arbitrary Lagrangian‐Eulerian (ALE) moving mesh formulations in the context of FSI. The structure, as commonly given in Lagrangian description, is surrounded by a fine resolved layer of fluid elements based on an ALE‐framework. This ALE‐fluid patch, which is embedded in a Eulerian background fluid domain, follows the deformation and motion of the structural interface. This approximation technique is not limited to finite element methods but can also be realized within other frameworks like finite volume or discontinuous Galerkin methods. In this work, the surface coupling between the two disjoint fluid subdomains is imposed weakly using a stabilized Nitsche's technique in a cut finite element method (CutFEM) framework. At the fluid‐solid interface, standard weak coupling of node‐matching or nonmatching finite element approximations can be utilized. As the fluid subdomains can be meshed independently, a sufficient mesh quality in the vicinity of the common fluid‐structure interface can be assured. To our knowledge, the proposed method is the only method (despite some overlapping domain decomposition approaches that suffer from other issues) that allows for capturing boundary layers and flow detachment via appropriate grids around largely moving and deforming bodies. In contrast to other methods, it is possible to do this, eg, without the necessity of costly remeshing procedures. A clear advantage over existing overlapping domain decomposition methods consists in the sharp splitting of the fluid domain, which comes along with improved convergence behavior of the resulting monolithic FSI system. In addition, it might also help to save computational costs as now background grids can be much coarser. Various FSI‐cases of rising complexity conclude the work. For validation purpose, results have been compared to simulations using a classical ALE‐fluid description or purely fixed‐grid CutFEM‐based schemes.