On the role of (weak) compressibility for fluid‐structure interaction solvers

Spina, Andrea La; Förster, Ch.; Kronbichler, Martin; Wall, Wolfgang A.

doi:10.1002/fld.4776

Cited by 12 publications

(12 citation statements)

References 30 publications

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“…27 Since then, it has been widely used and become a standard technique to handle moving domains in fluid-structure interaction (FSI) simulations. [28][29][30] More recent FSI simulations relying on this approach are presented in the work of Spenke et al, 31 La Spina et al, 32 and Liu et al 33 Furthermore, EMUM has been used in the context of free-surface flows 34 and to update finite element meshes according to prescribed boundary displacements. 35 The four-dimensional extension of EMUM (4DEMUM) presented in Section 3 allows us to obtain boundary-conforming pentatope meshes of complex geometries.…”

Section: F I G U R Ementioning

confidence: 99%

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Danwitz

Antony

Key

et al. 2021

Numerical Methods in Fluids

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Considering the flow through biological or engineered valves as an example, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behavior, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the application‐specific space‐time geometry as a contiguous computational domain. In this work, we obtain a boundary‐conforming discretization of the space‐time domain with four‐dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four‐dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space‐time meshes for domains with time‐variant topology is demonstrated in a valve simulation, and a flow simulation inspired by a clamped artery.

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Section: F I G U R Ementioning

confidence: 99%

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Danwitz

Antony

Key

et al. 2021

Numerical Methods in Fluids

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“…Equation (4) has been considered for numerical simulations of weakly compressible flows in long tubes, such as waxy crude oil [52] and polymer extrusion [50]. Though equation ( 4) is very attractive for its simplicity, other pressure-density relations have been used in literature, like the Murnaghan-Tait model [32].…”

Section: Governing Equationsmentioning

confidence: 99%

“…This represents a popular partitioned scheme for the solution of FSI problems and it has been used and analyzed for instance in [8,31]. In [32] it has moreover been shown that the introduction of a weak compressibility in the fluid field alleviates the constraints of the instability condition of the artificial added mass effect and, in comparison to a fully incompressible solver, it reduces the number of coupling iterations required and it leads to an increase of the dynamic relaxation parameter.…”

Section: A Partitioned Dirichlet-neumann Algorithm For the Hdg-cg Cou...mentioning

confidence: 99%

“…In particular, these schemes are affected by a detrimental phenomenon, defined in literature "artificial added mass effect" and analyzed in [3,14] in the context of incompressible flows. In a recent work [32], it is analytically demonstrated how the introduction of a weak compressibility in the fluid formulation alleviates the constraints of the instability condition of the artificial added mass effect, thanks to the reduction of the maximal eigenvalue of the so-called added mass operator. Moreover, in comparison to a fully incompressible solver, a significant reduction of the coupling iterations and the computational time is observed.…”

Section: Introductionmentioning

confidence: 99%

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A weakly compressible hybridizable discontinuous Galerkin formulation for fluid-structure interaction problems

La Spina,

Kronbichler,

Giacomini

et al. 2020

Preprint

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A scheme for the solution of fluid-structure interaction (FSI) problems with weakly compressible flows is proposed in this work. A novel hybridizable discontinuous Galerkin (HDG) method is derived for the discretization of the fluid equations, while the standard continuous Galerkin (CG) approach is adopted for the structural problem. The chosen HDG solver combines robustness of discontinuous Galerkin (DG) approaches in advection-dominated flows with higher order accuracy and efficient implementations. Two coupling strategies are examined in this contribution, namely a partitioned Dirichlet-Neumann scheme in the context of hybrid HDG-CG discretizations and a monolithic approach based on Nitsche's method, exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions. Numerical experiments show optimal convergence of the HDG and CG primal and mixed variables and superconvergence of the postprocessed fluid velocity. The robustness and the efficiency of the proposed weakly compressible formulation, in comparison to a fully incompressible one, are also highlighted on a selection of two and three dimensional FSI benchmark problems.

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“…Since then, it has been widely used and become a standard technique to handle moving domains in fluid-structure interaction (FSI) simulations [27,28,29]. Also, very recent FSI simulations rely on it [30,31,32]. Furthermore, EMUM has been used in the context of free-surface flows (for example in [33]) and to update finite element meshes according to prescribed boundary displacements (for example in [34]).…”

Section: Introduction and Problem Definitionmentioning

confidence: 99%

Four-Dimensional Elastically Deformed Simplex Space-Time Meshes for Domains with Time Variant Topology

von Danwitz,

Antony,

Key

et al. 2020

Preprint

View full text Add to dashboard Cite

Thinking of the flow through biological or technical valves, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behaviour, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the space-time extent of the application as a contiguous computational domain. In this work, we obtain a boundary conforming discretization of the spacetime domain with four-dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four-dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space-time meshes for domains with time variant topology is demonstrated in a valve simulation and a flow simulation inspired by a clamped artery.

show abstract

On the role of (weak) compressibility for fluid‐structure interaction solvers

Cited by 12 publications

References 30 publications

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

Four‐dimensional elastically deformed simplex space‐time meshes for domains with time‐variant topology

A weakly compressible hybridizable discontinuous Galerkin formulation for fluid-structure interaction problems

Four-Dimensional Elastically Deformed Simplex Space-Time Meshes for Domains with Time Variant Topology

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