A stabilized Nitsche‐type extended embedding mesh approach for 3D low‐ and high‐Reynolds‐number flows

Schott, Benedikt; Shahmiri, Shadan; Kruse, Raphael; Wall, Wolfgang A.

doi:10.1002/fld.4218

Cited by 19 publications

(63 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A spatial semidiscrete cut finite element formulation of , which utilizes a stabilizing residual‐based variational multiscale (RBVM) concept in the interior of the domain, ie, SUPG/PSPG/LSIC terms (see, eg, the works of Gresho and Sani and Hughes et al) and ghost penalty (GP) terms in the boundary zone, is based on previous works and reads as follows.…”

Section: Finite Element Formulations—different Spatial Discretizationsmentioning

confidence: 99%

“…Studies on the proposed GP terms comprised in

{scriptG}_{h}^{GP}

can be found also in the cited works. Applications successfully utilizing this technique can be found, for example, in the works of Schott et al…”

Section: Finite Element Formulations—different Spatial Discretizationsmentioning

confidence: 99%

“…A Nitsche‐based Cut FEM for Stokes flow interacting with linear elastic structures has been analyzed in the work of Burman and Fernández . A comparison of various coupling strategies of an incompressible fluid with immersed thin‐walled structures has been recently provided in the work of Alauzet et al Moreover, different formulations applicable to fixed‐grid methods based on utilizing an additional embedded fluid patch, which fits to the fluid‐structure interface but overlaps with a fixed background fluid grid in an unfitted fashion, have been developed in the works of Massing et al, Shahmiri et al, and Schott et al…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Schott

Ager

Wall

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Finite Element Formulations—different Spatial Discretizationsmentioning

confidence: 99%

“…Studies on the proposed GP terms comprised in

{scriptG}_{h}^{GP}

can be found also in the cited works. Applications successfully utilizing this technique can be found, for example, in the works of Schott et al…”

Section: Finite Element Formulations—different Spatial Discretizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Schott

Ager

Wall

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Definition For the weak coupling of the two subdomain approximations on

{scriptT}_{h}^{{normalf}_{1}}

and

{scriptT}_{h}^{{normalf}_{2}}

, specified by the coupling constraints , the stabilized Nitsche‐type formulation from the work of Schott et al is applied, which is comprised in the following coupling operator:

{scriptC}_{h}^{{normalf}_{1} {normalf}_{2}} ((), ((), U_{h}^{1}, U_{h}^{2}), ((), V_{h}^{1}, V_{h}^{2})) = - {(⟨⟩, 2 μ^{normalf} bold-italicϵ ((), {bold-italicu}_{h}^{{normalf}_{2}}) {bold-italicn}^{{normalf}_{1} {normalf}_{2}}, ⟦ {bold-italicv}_{h} ⟧)}_{{normalΓ}^{{normalf}_{1} {normalf}_{2}}} + {(⟨⟩, p_{h}^{{normalf}_{2}}, ⟦ {bold-italicv}_{h} ⟧ \cdot {bold-italicn}^{{normalf}_{1} {normalf}_{2}})}_{{normalΓ}^{{normalf}_{1} {normalf}_{2}}}

+ (⟨⟩, ⟦ {bold-italicu}_{h} ⟧, 2 μ^{normalf} bold-italicϵ ((), {bold-italicv}_{h}^{{normalf}_{2}}) {bold-italicn}^{{normalf}_{1} normalf})

…”

Section: A Cutfem‐based Hybrid Fsi Formulationmentioning

confidence: 99%

“…Concerning detailed accuracy, stability, and convergence results of the single key ingredients of this novel hybrid method, at this point, we would like to refer the interested reader to important and helpful preceding publications. The C ut FEM‐based fluid‐fluid coupling has been already investigated in the work of Schott et al in very detail. The latter includes numerical results for different Nitsche weighting and penalty variants, detailed convergence results in a large range of mesh sizes in two and three spatial dimensions.…”

Section: Numerical Examplesmentioning

confidence: 99%

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

Schott

Ager

Wall

2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard 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.

show abstract

Combining boundary‐conforming finite element meshes on moving domains using a sliding mesh approach

Helmig

Key

Behr

et al. 2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

For most finite element simulations, boundary‐conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a boundary‐conforming mesh becomes more difficult and time consuming. One might therefore decide to resort to an approach where individual boundary‐conforming meshes are pieced together in a modular fashion to form a larger domain. This article presents a stabilized finite element formulation for fluid and temperature equations on sliding meshes. It couples the solution fields of multiple subdomains whose boundaries slide along each other on common interfaces. Thus, the method allows to use highly tuned boundary‐conforming meshes for each subdomain that are only coupled at the overlapping boundary interfaces. In contrast to standard overlapping or fictitious domain methods the coupling is broken down to few interfaces with reduced geometric dimension. The formulation consists of the following key ingredients: the coupling of the solution fields on the overlapping surfaces is imposed weakly using a stabilized version of Nitsche's method. It ensures mass and energy conservation at the common interfaces. Additionally, we allow to impose weak Dirichlet boundary conditions at the nonoverlapping parts of the interfaces. We present a detailed numerical study for the resulting stabilized formulation. It shows optimal convergence behavior of the interface coupling for both Newtonian and generalized Newtonian material models. Simulations of flow of plastic melt inside single‐screw as well as twin‐screw extruders demonstrate the applicability of the method to complex and relevant industrial applications.

show abstract

A stabilized Nitsche‐type extended embedding mesh approach for 3D low‐ and high‐Reynolds‐number flows

Cited by 19 publications

References 50 publications

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

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

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

Combining boundary‐conforming finite element meshes on moving domains using a sliding mesh approach

Contact Info

Product

Resources

About