zbMATH — the first resource for mathematics

Non-Newtonian flow in branched pipes and artery models. (English) Zbl 1198.76163
Summary: This work concerns finite element analysis for a class of generalized Newtonian flows through branching pipe or tube junctions in industrial applications or blood flow through arterial branches, prosthetic tube implants or in biomedical engineering devices. A two-step morphing transformation is developed and implemented to map a generic coplanar 3D branching flow configuration to general out-of-plane deformed geometry including local constriction/dilation ‘defects’ suitable for modeling specific arterial flow and industrial flow applications. Unstructured 3D meshes may be generated in the reference configuration and morphed to the application configuration. The resulting meshes may be tangled and exhibit mesh quality degradation. Algorithms integrating mesh generation, morphing, untangling and cell shape control strategies are presented.
Phenomenological studies are conducted with the Powell-Eyring class as a representative model to determine local details of shear-thinning flow behavior as well as the nature and location of high shear stress regions on artery branch walls. The supporting simulations are carried out using a parallel finite element scheme with domain decomposition by a sectional partitioning that takes advantage of the medial curve shape and specialized ILU preconditioning.

76Z05 Physiological flows
76A05 Non-Newtonian fluids
76M10 Finite element methods applied to problems in fluid mechanics
92C35 Physiological flow
CUBIT; libMesh
Full Text: DOI
[1] Haselton, Journal of Fluid Mechanics 123 pp 315– (1982)
[2] Liepsch, Advances in Bioengineering 22 pp 277– (1992)
[3] Gijsen, Journal of Biomedics 32 pp 601– (1999)
[4] Mijovic, Technology and Health Care Archive 11 pp 115– (2003)
[5] Miller, Communications in Numerical Methods in Engineering 23 pp 121– (2007)
[6] Ree, Journal of Applied Physics 26 pp 800– (1955)
[7] Eyring, Journal of Chemical Physics 4 pp 283– (1936)
[8] Cramer, AIChE Journal 14 pp 980– (1968)
[9] . Finite element approximations of generalized Newtonian fluids. Technical Report, TICAM, The University of Texas at Austin, 2001.
[10] , , , . Distributed parallel simulation of surface tension driven viscous flow and transport processes. Computational Fluid Dynamics: Proceedings of the Fourth UNAM Supercomputing Conference, Mexico City, Mexico, UNAM, June 2000; 143–155.
[11] , , . Parallel distributed solution of viscous flow with heat transfer on workstation clusters. High Performance Computing ’00 Proceedings, Washington, DC, April 2000.
[12] , , . Finite element modeling of generalised Newtonian flows. Proceedings of the 14th Australasian Fluids Conference, Adelaide, December 2001.
[13] Simulation of non-Newtonian fluids on workstation clusters. Ph.D. Thesis, The University of Texas at Austin, May 2004.
[14] Cubit Mesh Generation Toolkit. 2008. Available from:http://cubit.sandia.gov/.
[15] A variational grid optimization method based on a local cell quality metric. Ph.D. Thesis, The University of Texas at Austin, August 2005.
[16] Ree, Journal of Applied Physics 26 pp 793– (1955)
[17] Ree, Industrial Engineering and Chemistry 50 pp 1036– (1958)
[18] Carey, International Journal for Numerical Methods in Fluids 46 pp 1211– (2004)
[19] Russell, Industrial and Engineering Chemistry, Process Design and Development 13 pp 391– (1974)
[20] Christiansen, Transactions of the Society of Rheology 10 pp 419– (1966)
[21] Barth, International Journal for Numerical Methods in Fluids 54 pp 1313– (2007)
[22] Griffiths, International Journal for Numerical Methods in Fluids 24 pp 393– (1997)
[23] Bose, Computer Methods in Applied Mechanics and Engineering 180 pp 431– (2000)
[24] Yagawa, International Journal for Numerical Methods in Fluids 7 pp 521– (1986)
[25] , , . Thin network extraction in 3d images: application to medical angiograms. Proceedings of the International Conference on Pattern Recognition, Vienna, Austria, 1996; 386–390.
[26] Klein, IEEE Transactions on Medical Imaging 16 pp 468– (1997)
[27] , , . Characteristics measurement for blood vessel diseases detection based on cone-beam CT images. IEEE Nuclear Science Symposium and Medical Imaging Conference, San Francisco, CA, vol. 3, 1995; 1660–1664.
[28] libMesh: A c++ Finite Element Library. 2008. Available from: http://libmesh.sourceforge.net/.
[29] Computational Grids: Generation, Adaptation, and Solution Strategies. Taylor and Francis: London, 1997.
[30] . A local cell quality metric and variational grid smoothing algorithm. Proceedings of the 12th International Meshing Roundtable, Santa Fe, NM, 2003; 371–378.
[31] Branets, Engineering with Computers 21 pp 19– (2005)
[32] . Smoothing and adaptive redistribution for grids with irregular valence and hanging nodes. Proceedings of the 13th International Meshing Roundtable, Williamsburg, VA, 2004; 333–344.
[33] Biomechanics of Brain for Computer Integrated Surgery. Warsaw University of Technology Publishing House: Warsaw, 2002.
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.