A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state

Takizawa, Kenji; Tezduyar, Tayfun E.; Avsar, Reha

doi:10.1007/s00466-020-01835-z

Cited by 42 publications

(45 citation statements)

References 165 publications

(386 reference statements)

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“…Mesh relaxation and mesh moving methods based on fiberreinforced hyperelasticity and optimized ZSS were introduced in [28]. The methods have been developed targeting isogeometric discretization but are also applicable to finite element discretization.…”

Section: Mesh Relaxation Based On Fiber-reinforced Hyperelasticity Anmentioning

confidence: 99%

“…The constitutive models and parameters can be defined individually for the elements or mesh regions. For more on the method, see [28].…”

Section: Mesh Relaxation Based On Fiber-reinforced Hyperelasticity Anmentioning

confidence: 99%

“…To improve the mesh quality, we use the mesh relaxation method introduced in [28], which is based on fiber-reinforced hyperelasticity and optimized ZSS. The hyperelasticity model is the one given by Eqs.…”

Section: Casementioning

confidence: 99%

“…The hyperelasticity model is the one given by Eqs. (48), (39), (50) and (51) in [28], with κ = 0. The material properties are κ B = 10 −2 , β B = 2, μ = 1, C 1 = 100, and C 2 = 10 −2 .…”

Section: Casementioning

confidence: 99%

“…The three special methods are the ST Slip Interface (ST-SI) method [19,20], ST Isogeometric Analysis (ST-IGA) [16,21,22], and the ST/NURBS Mesh Update Method (STNMUM) [21,[23][24][25]. The mesh-related methods are a general-purpose NURBS mesh generation method [26,27] and a mesh relaxation method [28] based on fiberreinforced hyperelasticity and optimized zero-stress state (ZSS).…”

Section: Introductionmentioning

confidence: 99%

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Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine

et al. 2020

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We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space-time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

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Section: Mesh Relaxation Based On Fiber-reinforced Hyperelasticity Anmentioning

confidence: 99%

“…The constitutive models and parameters can be defined individually for the elements or mesh regions. For more on the method, see [28].…”

Section: Mesh Relaxation Based On Fiber-reinforced Hyperelasticity Anmentioning

confidence: 99%

Section: Casementioning

confidence: 99%

Section: Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine

et al. 2020

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

Helmig

Key

Behr

et al. 2020

Numerical Methods in Fluids

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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.

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Space–Time Computational FSI and Flow Analysis: 2004 and Beyond

Tezduyar

Takizawa

Kuraishi

2022

Current Trends and Open Problems in Computational Mechanics

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A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state

Cited by 42 publications

References 165 publications

Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine

Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine

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

Space–Time Computational FSI and Flow Analysis: 2004 and Beyond

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