A three-field formulation for incompressible viscoelastic fluids

Copley, 1970, Rheogoniometric viscosity measurements of whole human blood at minimal sheaer rates down to 0.0009s−1, Cell. Mol. Life Sci., 26, 904, 10.1007/BF02114252 Thurston, 1979, Rheological parameters for the viscosity viscoelasticity and thixotropy of blood, Biorheology, 16, 149, 10.3233/BIR-1979-16303 Fung, 1997 Rajagopal, 1993, Mechanics of non-Newtonian fluids – recent developments in theoretical fluids mechanics, 291, 129 Anand, 2004, A shear-thinning viscoelastic fluid model for describing the flow of blood, Int. J. Cardiovas. Med. Sci., 4, 59 Anand, 2003, A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood, Comput. Math. Methods Med., 5, 183 Rajagopal, 2000, A thermodynamic frame work for rate type fluid models, J. Non-Newtonian Fluid Mech., 88, 207, 10.1016/S0377-0257(99)00023-3 Yeleswarapu, 1998, The flow of blood in tubes: theory and experiment, Mech. Res. Commun., 25, 257, 10.1016/S0093-6413(98)00036-6 Baaijens, 1998, Mixed finite element methods for viscoelastic flow analysis: a review, J. Non-Newtonian Fluid Mech., 79, 361, 10.1016/S0377-0257(98)00122-0 Coronado, 2006, Four-field Galerkin/least-squares formulation for viscoelastic fluids, J. Non-Newtonian Fluid Mech., 140, 132, 10.1016/j.jnnfm.2006.03.016 Fortin, 1989, A new approach for the FEM simulation of viscoelastic flows, J. Non-Newtonian Fluid Mech., 32, 295, 10.1016/0377-0257(89)85012-8 Guénette, 1995, A new mixed finite element method for computing viscoelastic flows, J. Non-Newtonian Fluid Mech., 60, 27, 10.1016/0377-0257(95)01372-3 Hulsen, 2005, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech., 127, 27, 10.1016/j.jnnfm.2005.01.002 Reddy, 2000 Sun, 1996, An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG, J. Non-Newtonian Fluid Mech., 65, 75, 10.1016/0377-0257(96)01448-6 Sun, 1999, Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG, J. Non-Newtonian Fluid Mech., 86, 281, 10.1016/S0377-0257(98)00176-1 Bazilevs, 2006, Isogeometric fluid-structure interaction analysis with applications to arterial blood flow, Comput. Mech., 38, 310, 10.1007/s00466-006-0084-3 Ku, 2002, In vivo validation of numerical predictions of blood flow in arterial bypass grafts, Ann. Biomed. Eng., 30, 743, 10.1114/1.1496086 Perktold, 2003, Computational models of arterial flow and mass transport, 73 Perktold, 1995, Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model, J. Biomech., 28, 845, 10.1016/0021-9290(95)95273-8 Taylor, 2002, In vivo quantification of blood flow and wall shear stress in the human abdominal aorta during lower limb exercise, Ann. Biomed. Eng., 30, 402, 10.1114/1.1476016 Taylor, 1998, Finite element modeling of blood flow in arteries, Comput. Methods Appl. Mech. Eng., 158, 155, 10.1016/S0045-7825(98)80008-X Tezduyar, 2008, Arterial fluid mechanics modeling with the stabilized space-time fluid-structure interaction technique, Int. J. Numer. Methods Fluids, 57, 601, 10.1002/fld.1633 Zhang, 2007, Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Comput. Methods Appl. Mech. Eng., 196, 2943, 10.1016/j.cma.2007.02.009 Rajagopalan, 1990, viscoelastic flow using constitutive equations with a Newtonian viscosity, J. Non-Newtonian Fluid Mech., 36, 159, 10.1016/0377-0257(90)85008-M Rajagopalan, 1990, viscoelastic flow using a multimode Maxwell model: application of the explicitly elliptic momentum equation (EEME) formulation, J. Non-Newtonian Fluid Mech., 36, 135, 10.1016/0377-0257(90)85007-L Marchal, 1987, A new mixed finite element for calculating viscoelastic flow, J. Non-Newtonian Fluid Mech., 26, 77, 10.1016/0377-0257(87)85048-6 Brezzi, 1997, b=∫g, Comput. Methods Appl. Mech. Eng., 145, 329, 10.1016/S0045-7825(96)01221-2 Franca, 2006, Revisiting stabilized finite element methods for the advective–diffusive equation, Comput. Methods Appl. Mech. Eng., 195, 1560, 10.1016/j.cma.2005.05.028 Hughes, 1995, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Eng., 127, 387, 10.1016/0045-7825(95)00844-9 Hughes, 1998, The variational multiscale method – a paradigm for computational mechanics, Comput. Methods Appl. Mech. Eng., 166, 3, 10.1016/S0045-7825(98)00079-6 Masud, 2008, A hierarchical multiscale framework for problems with multiscale source terms, Comput. Methods Appl. Mech. Eng., 197, 2692, 10.1016/j.cma.2007.12.024 Masud, 2010, A Heterogeneous Multiscale Modeling Framework for Hierarchical Systems of Partial Differential Equations, Int. J. Numer. Meth. Fluids Masud, 2006, A multiscale finite element method for the incompressible Navier–Stokes equation, Comput. Methods Appl. Mech. Eng., 195, 1750, 10.1016/j.cma.2005.05.048 Masud, 2009, A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations, Comput. Mech., 44, 145, 10.1007/s00466-008-0362-3 Masud, 2010, A stabilized mixed finite element method for the incompressible shear-rate dependent non-Newtonian fluids: Variational Multiscale framework and consistent linearization, Comp. Methods Appl. Mech. Eng. Ghia, 1982, High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method, J. Comput. Phys., 48, 387, 10.1016/0021-9991(82)90058-4