Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

Bazilevs, Yuri; Michler, Christian; Calo, Victor M.; Hughes, Thomas J.R.

doi:10.1016/j.cma.2008.11.020

Cited by 253 publications

(190 citation statements)

References 39 publications

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“…Isogeometric analysis [27,9] is a computational mechanics technology which uses basis functions emanating from computer aided geometric design, such as B-Splines, NURBS, T-splines or subdivision surfaces instead of traditional and provides a general framework towards this purpose. Extensive investigations including fluid-solid interaction [3,2], the extended finite element method [5] and electromagnetics [8] have additionally demonstrated the ability of isogeometric analysis to provide not only more precise geometric representations than traditional finite elements but also efficient approaches to problems such as phase-field descriptions [16,17] and rotationless thin shell formulations [31,4]. These advantages are complemented by recent developments that allow a local refinement of the geometry description and consequently of the solution space through T-splines [11,52,53] -see also Borden et al [7] for an application.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Temizer

Wriggers

Hughes

2012

Computer Methods in Applied Mechanics and Engineering

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157

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a b s t r a c tA three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS is presented in the finite deformation regime. Within a setting where the NURBS discretization of the contact surface is inherited directly from the NURBS discretization of the volume, the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities. The formulation delivers a non-negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative Lagrange discretizations independent of the discretization order. These enable the achievement of improved smoothness in global contact forces and moments through higher-order geometrical descriptions. It is concluded that the presented mortar-based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Temizer

Wriggers

Hughes

2012

Computer Methods in Applied Mechanics and Engineering

Self Cite

157

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“…IGA has been successfully employed in many areas of engineering and sciences, such as fluid mechanics and turbulence [29][30][31][32][33][34][35][36][37][38], solid and structural mechanics [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55], fluid-structure interaction [13,[56][57][58][59][60][61][62][63], phase-field modeling [64][65][66][67][68], complex fluids [69,70], Lagrangian shock hydrodynamics [71,72], contact mechanics [16,[73][74][75][76]…”

Section: Introductionmentioning

confidence: 99%

An interactive geometry modeling and parametric design platform for isogeometric analysis

Hsu

Wang

Herrema

et al. 2015

Computers & Mathematics with Applications

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In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. KeywordsIsogeometric analysis, NURBS and T-splines, Parametric design, Rhino and Grasshopper, Visual programming, Graphical generative algorithms RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. Authors Ming-Chen

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“…Previous work on weak enforcement of essential boundary conditions also includes the pioneering effort of NITSCHE [38] for the Poisson problem which has been successfully adapted to structural mechanics [25,22,27,20], biomechanics [44], and fluid mechanics [12,11]. Besides being computationally convenient, weakly enforced boundary conditions show a significant increase in accuracy over their strongly imposed counterparts for wall-bounded turbulent flows [12]. In this framework, the focus of the present paper is on the application of the weak boundary conditions within the finite cell method.…”

Section: Introductionmentioning

confidence: 99%

“…The maximum eigenvalues of the cell-wise evaluation of (30) range corresponded to the polynomial degree (p = 3) and the cell contribution to the physical domain Ω in the interval [12,24]. A choice of C (S,N ) = 4 max λ (S,N ) , respectively, for the cut boundary cells provided an error level of e E Ω ≈ 10% (error in energy norm).…”

Section: Plane Stress Annular Platementioning

confidence: 99%

Weakly enforced essential boundary conditions for NURBS‐embedded and trimmed NURBS geometries on the basis of the finite cell method

Ruess

Schillinger

Bazilevs

et al. 2013

Numerical Meth Engineering

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150

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Enforcing essential boundary conditions plays a central role in immersed boundary methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints. We formulate an extension of Nitsche's method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the B-spline and NURBS-version of the finite cell method or isogeometric analysis on trimmed geometries. Furthermore, we illustrate a significant improvement of the flexibility and applicability of this extension in the modelling process of complex 3D geometries. With several benchmark problems we demonstrate the overall good convergence behavior of the proposed method and its good accuracy. We provide extensive studies on the stability of the method, its influence parameters and numerical properties, and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two. A newly composed boundary integration concept further enhances the modelling process and allows a flexible, discretization-independent introduction of boundary conditions. Finally, we present our strategy in the framework of the modelling and isogeometric analysis process of trimmed NURBS geometries.

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Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

Cited by 253 publications

References 39 publications

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS

An interactive geometry modeling and parametric design platform for isogeometric analysis

Weakly enforced essential boundary conditions for NURBS‐embedded and trimmed NURBS geometries on the basis of the finite cell method

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