NURBSbased isogeometric analysis for the computation of flows about rotating components
 Y. Bazilevs,
 T. J. R. Hughes
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The ability of nonuniform rational Bsplines (NURBS) to exactly represent circular geometries makes NURBSbased isogeometric analysis attractive for applications involving flows around and/or induced by rotating components (e.g., submarine and surface ship propellers). The advantage over standard finite element discretizations is that rotating components may be introduced into a stationary flow domain without geometric incompatibility. Although geometric compatibility is exactly achieved, the discretization of the flow velocity and pressure remains incompatible at the interface between the stationary and rotating subdomains. This incompatibility is handled by using a weak enforcement of the continuity of solution fields at the interface of the stationary and rotating subdomains.
 Akkerman, I, Bazilevs, Y, Calo, VM, Hughes, TJR, Hulshoff, S (2008) The role of continuity in residualbased variational multiscale modeling of turbulence. Comput Mech 41: pp. 371378 CrossRef
 Arnold, DN, Brezzi, F, Cockburn, B, Marini, LD (2002) Unified analysis of Discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39: pp. 17491779 CrossRef
 Barenblatt, GI (1979) Similarity, selfsimilarity, and intermediate assymptotics. Consultants Bureau, Plenum Press, New York and London
 Bazilevs, Y, Calo, VM, Zhang, Y, Hughes, TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: pp. 310322 CrossRef
 Bazilevs, Y, Calo, VM, Cottrell, JA, Hughes, TJR, Reali, A, Scovazzi, G (2007) Variational multiscale residualbased turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: pp. 173201 CrossRef
 Bazilevs, Y, Beirao da Veiga, L, Cottrell, JA, Hughes, TJR, Sangalli, G (2006) Isogeometric analysis: approximation, stability and error estimates for hrefined meshes. Math Models Methods Appl Sci 16: pp. 10311090 CrossRef
 Bazilevs, Y, Hughes, TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: pp. 1226 CrossRef
 Bazilevs, Y, Michler, C, Calo, VM, Hughes, TJR (2007) Weak Dirichlet boundary conditions for wallbounded turbulent flows. Comput Methods Appl Mech Eng 196: pp. 48534862 CrossRef
 Behr, M, Tezduyar, T (1999) Shearslip mesh update method. Comput Methods Appl Mech Eng 174: pp. 261274 CrossRef
 Behr, M, Tezduyar, T (2001) Shearslip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190: pp. 31893200 CrossRef
 Brooks, AN, Hughes, TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32: pp. 199259 CrossRef
 Chung, J, Hulbert, GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalizedα method. J Appl Mech 60: pp. 37175 CrossRef
 Cohen, E, Riesenfeld, R, Elber, G (2001) Geometric modeling with splines: an introduction. A. K. Peters Ltd, Wellesley
 Cottrell, JA, Reali, A, Bazilevs, Y, Hughes, TJR (2006) Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195: pp. 52575297 CrossRef
 Ern, A, Guermond, JL (2004) Theory and practice of finite elements. Springer, Berlin
 Farin, GE (1995) NURBS curves and surfaces: from projective geometry to practical use. A. K. Peters, Ltd, Natick
 Hansbo, P, Hermansson, J (2003) Nitsche’s method for coupling nonmatching meshes in fluid–structure vibration problems. Comput Mech 32: pp. 134139 CrossRef
 Hansbo, P, Hermansson, J, Svedberg, T (2004) Nitsche’s method combined with spacetime finite elements for ALE fluid–structure interaction problems. Comput Methods Appl Mech Eng 193: pp. 41954206 CrossRef
 Houzeaux, G, Codina, R (2003) A chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations. Comput Methods Appl Mech Eng 192: pp. 33433377 CrossRef
 Hughes, TJR, Feijóo, G, Mazzei, L, Quincy, JB (1998) The variational multiscale method—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166: pp. 324 CrossRef
 Hughes, TJR, Mallet, M (1986) A new finite element formulation for fluid dynamics. III. The generalized streamline operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58: pp. 305328 CrossRef
 Hughes, TJR, Cottrell, JA, Bazilevs, Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: pp. 41354195 CrossRef
 Hughes, TJR, Sangalli, G (2007) Variational multiscale analysis: the finescale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45: pp. 539557 CrossRef
 Jansen, KE, Whiting, CH, Hulbert, GM (1999) A generalizedα method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: pp. 305319 CrossRef
 Piegl, L, Tiller, W (1997) The NURBS book (Monographs in visual communication). Springer, New York
 Rogers, DF (2001) An introduction to NURBS with historical perspective. Academic Press, San Diego
 Shakib, F, Hughes, TJR, Johan, Z (1991) A new finite element formulation for computational fluid dynamics. X. The compressible Euler and Navier–Stokes equations. Comput Methods Appl Mech Eng 89: pp. 141219 CrossRef
 Texas Advanced Computing Center (TACC). http://www.tacc.utexas.edu
 Tezduyar, T, Aliabadi, S, Behr, M, Johnson, A, Kalro, V, Litke, M (1996) Flow simulation and high performance computing. Comput Mech 18: pp. 397412 CrossRef
 Tezduyar, TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: pp. 555575 CrossRef
 Wheeler, MF (1978) An elliptic collocation—finite element method with interior penalties. SIAM J Numer Anal 15: pp. 152161 CrossRef
 Wriggers, P, Zavarise, G (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41: pp. 407420 CrossRef
 Title
 NURBSbased isogeometric analysis for the computation of flows about rotating components
 Journal

Computational Mechanics
Volume 43, Issue 1 , pp 143150
 Cover Date
 20081201
 DOI
 10.1007/s004660080277z
 Print ISSN
 01787675
 Online ISSN
 14320924
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Fluids
 Navier–Stokes equations
 Rotating components
 NURBS
 Isogeometric analysis
 Industry Sectors
 Authors

 Y. Bazilevs ^{(1)}
 T. J. R. Hughes ^{(1)}
 Author Affiliations

 1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX, 78712, USA