×

zbMATH — the first resource for mathematics

NURBS-based isogeometric analysis for the computation of flows about rotating components. (English) Zbl 1171.76043
Summary: The ability of non-uniform rational B-splines (NURBS) to exactly represent circular geometries makes NURBS-based 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 stationary and rotating subdomains.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Akkerman I, Bazilevs Y, Calo VM, Hughes TJR, Hulshoff S (2008) The role of continuity in residual-based variational multiscale modeling of turbulence. Comput Mech 41: 371–378 · Zbl 1162.76355
[2] Arnold DN, Brezzi F, Cockburn B, Marini LD (2002) Unified analysis of Discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39: 1749–1779 · Zbl 1008.65080
[3] Barenblatt GI (1979) Similarity, self-similarity, and intermediate assymptotics. Consultants Bureau, Plenum Press, New York and London
[4] Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322 · Zbl 1161.74020
[5] Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201 · Zbl 1169.76352
[6] Bazilevs Y, Beirao da Veiga L, Cottrell JA, Hughes TJR, Sangalli G (2006) Isogeometric analysis: approximation, stability and error estimates for h-refined meshes. Math Models Methods Appl Sci 16: 1031–1090 · Zbl 1103.65113
[7] Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12–26 · Zbl 1115.76040
[8] Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196: 4853–4862 · Zbl 1173.76397
[9] Behr M, Tezduyar T (1999) Shear-slip mesh update method. Comput Methods Appl Mech Eng 174: 261–274 · Zbl 0959.76037
[10] Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190: 3189–3200 · Zbl 1012.76042
[11] 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: 199–259 · Zbl 0497.76041
[12] Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-{\(\alpha\)} method. J Appl Mech 60: 371–75 · Zbl 0775.73337
[13] Cohen E, Riesenfeld R, Elber G (2001) Geometric modeling with splines: an introduction. A. K. Peters Ltd, Wellesley · Zbl 0980.65016
[14] Cottrell JA, Reali A, Bazilevs Y, Hughes TJR (2006) Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195: 5257–5297 · Zbl 1119.74024
[15] Ern A, Guermond J-L (2004) Theory and practice of finite elements. Springer, Berlin · Zbl 1059.65103
[16] Farin GE (1995) NURBS curves and surfaces: from projective geometry to practical use. A. K. Peters, Ltd, Natick · Zbl 0848.68112
[17] Hansbo P, Hermansson J (2003) Nitsche’s method for coupling non-matching meshes in fluid–structure vibration problems. Comput Mech 32: 134–139 · Zbl 1035.74055
[18] Hansbo P, Hermansson J, Svedberg T (2004) Nitsche’s method combined with space-time finite elements for ALE fluid–structure interaction problems. Comput Methods Appl Mech Eng 193: 4195–4206 · Zbl 1175.74082
[19] 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: 3343–3377 · Zbl 1054.76049
[20] Hughes TJR, Feijóo G, Mazzei L, Quincy JB (1998) The variational multiscale method–a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166: 3–24 · Zbl 1017.65525
[21] 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: 305–328 · Zbl 0622.76075
[22] Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195 · Zbl 1151.74419
[23] Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45: 539–557 · Zbl 1152.65111
[24] Jansen KE, Whiting CH, Hulbert GM (1999) A generalized-{\(\alpha\)} method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305–319 · Zbl 0973.76048
[25] Piegl L, Tiller W (1997) The NURBS book (Monographs in visual communication), 2nd edn. Springer, New York · Zbl 0868.68106
[26] Rogers DF (2001) An introduction to NURBS with historical perspective. Academic Press, San Diego
[27] 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: 141–219
[28] Texas Advanced Computing Center (TACC). http://www.tacc.utexas.edu
[29] Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18: 397–412 · Zbl 0893.76046
[30] Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575 · Zbl 1032.76605
[31] Wheeler MF (1978) An elliptic collocation–finite element method with interior penalties. SIAM J Numer Anal 15: 152–161 · Zbl 0384.65058
[32] Wriggers P, Zavarise G (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41: 407–420 · Zbl 1162.74419
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.