Mittal, R. and Iaccarino, G.. Immersed boundary methods. Annual Review of Fluid Mechanics, 37, 239–261, 2005.
Balaras, E.. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations. Computers Fluids, 33, 375–404, 2004.
Parnaudeau, P., Carlier, J., Heitz, D., and Lamballais, E.. Experimental and numerical studies of the flow over a circular cylinder at reynolds number 3900. Physics of Fluids, 20 085101, 2008.
Yang, J., Preidikman, S., and Balaras, E.. A strongly coupled, embedded-boundary method for fluid-structure interactions of elastically mounted rigid bodies. Journal of Fluids and Structures, 24(2), 167–182, 2008.
Monasse, L., Daru, V., Mariotti, C., and Piperno, S.. A conservative immersed boundary method for fluid-structure interaction in the compressible inviscid case. Computational Fluid Dynamics 2010, Kuzmin, A. (Ed.), Springer, 2010.
De Tullio, M. D., Cristallo, A., Balaras, E., and Verzicco, R.. Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve. Journal of Fluid Mechanics, 622, 259–290, 2009.
Bergmann, M. and Iollo, A.. Modeling and simulation of fish-like swimming. Journal of Computational Physics, 230, 329–348, 2011.
Teran, J., Fauci, L., and Shelley, M.. Peristaltic pumping and irreversibility of a Stokesian viscoelastic fluid. Physics of Fluids, 20, 073101, 2008.
Nonaka, A., Trebotich, D., Miller, G. H., Graves, D. T., and Colella, P.. A higher-order upwind method for viscoelastic flow. Communications in Applied Mathematics and Computational Science, 4, 57–83, 2009.
Crochet, M. J., Davies, A. R., and Walters, K.. Numerical Simulation of Non-Newtonian Flow. Elsevier, Amsterdam, 1984.
Walters, K. and Webster, M. F.. The distinctive CFD challenges of computational rheology. International Journal For Numerical Methods in Fluid, 43, 577–596, 2003.
Owens, R. G. and Phillips, T. N.. Computational Rheology. Imperial College Press, London, 2002.
Kang, S., Iaccarino, G., and Moin, P.. Accurate and efficient immersed-boundary interpolations for viscous flows. In Center for Turbulence Research Briefs, NASA Ames/Stanford University, pp. 31–43, 2004.
Muldoon, F. and Acharya, S.. A divergence-free interpolation scheme for the immersed boundary method. International Journal for Numerical Methods in Fluids, 56, 1845–1884, 2008.
Guy, R. D. and Hartenstine, D. A.. On the accuracy of direct forcing immersed boundary methods with projection methods. Journal of Computational Physics, 229(7), 2479–2496, 2010.
Cheny, Y. and Botella, O.. An immersed boundary/level-set method for incompressible viscous flows in complex geometries with good conservation properties. European Journal of Mechanics, 18, 561–587, 2009.
Cheny, Y. and Botella, O.. The LS-STAG method: A new immersed boundary / level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties. Journal of Computational Physics, 229, 1043–1076, 2010.
Botella, O., Ait-Messaoud, M., Pertat, A., Rigal, C., and Cheny, Y.. The LS-STAG immersed boundary method for non-Newtonian flows in irregular geometries: Flow of shear-thinning liquids between eccentric rotating cylinders. Theoretical and Computational Fluid Dynamics, 29, 93–110, 2015.
Bird, R. B., Armstrong, R. C., and Hassager, O.. Dynamics of Polymeric Liquids. Wiley-Interscience, New-York, 1987.
Baaijens, F. P. T.. Mixed finite element methods for viscoelastic flow analysis: A review. Journal of Non-Newtonian Fluid Mechanics, 79, 361–385, 1998.
Darwish, M. S. and Whiteman, J. R.. Numerical modeling of viscoelastic liquids using a finite-volume method. Journal of Non-Newtonian Fluid Mechanics, 45, 311–337, 1992.
Gerritsma, M.. Time dependant numerical simulations of a viscoelastic fluid on a staggered grid. PhD thesis, University of Groningen, The Netherlands, 1996.
Van Kemenade, V. and Deville, M. O.. Application of spectral elements to viscoelastic creeping flows. Journal of Non-Newtonian Fluid Mechanics, 51(3), 277–308, 1994.
Fattal, R. and Kupferman, R.. Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. Journal of Non-Newtonian Fluid Mechanics, 126, 23–37, 2005.
Hao, J., Pan, T.-W., Glowinski, R., and Joseph, D. D.. A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: A positive definiteness preserving approach. Journal of Non-Newtonian Fluid Mechanics, 156, 95–111, 2009.
Matallah, H., Townsend, P., and Webster, M. F.. Recovery and stress-splitting schemes for viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, 75, 139–166, 1998.
Alves, M. A., Pinho, F. T., and Oliveira, P. J.. Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, 93, 287–314, 2000.
Kim, J. M., Kim, C., Kim, J. H., Chung, C., Ahn, K. H., and Lee, S. J.. High-resolution finite element simulation of 4:1 planar contraction flow of viscoelastic fluid. Journal of Non-Newtonian Fluid Mechanics, 129, 23–37, 2005.
Dupret, F., Marchal, J. M., and Crochet, M. J.. On the consequence of discretization errors in the numerical calculation of viscoelastic flow. Journal of Non-Newtonian Fluid Mechanics, 18, 173–186, 1985.
Aboubacar, M., Matallah, H., Tamaddon-Jahromi, H. R., and Webster, M. F.. Numerical prediction of extensional flows in contraction geometries: Hybrid finite volume/element method. Journal of Non-Newtonian Fluid Mechanics, 104, 125–164, 2002.
Phillips, T. N. and Williams, A. J.. Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method. Journal of Non-Newtonian Fluid Mechanics, 87, 215–246, 1999.
Yoo, J. Y. and Na, Y.. A numerical study of the planar contraction flow of a viscoelastic fluid using the SIMPLER algorithm. Journal of Non-Newtonian Fluid Mechanics, 39, 89–106, 1991.
Oliveira, P. J., Pinho, F. T., and Pinto, G. A.. Numerical simulation of non-linear elastic flows with a general collocated finite-volume method. Journal of Non-Newtonian Fluid Mechanics, 79, 1–43, 1998.
Keiller, R. A.. Entry-flow calculations for the Oldroyd-B and FENE equations. Journal of Non-Newtonian Fluid Mechanics, 46, 143–178, 1993.
Quinzani, L. M., Amstrong, R. C., and Brown, R. A.. Birefringence and laser-Doppler velocimetry (LDV) studies of viscoelastic flow through planar contraction. Journal of Non-Newtonian Fluid Mechanics, 52, 1–36, 1994.
Quinzani, L. M., Amstrong, R. C., and Brown, R. A.. Used of coupled birefringence and LDV studies of flow through planar contraction to test constitutive equations for concentrated polymer solutions. Journal of Rheology, 39, 1201–1228, 1995.
Harlow, F. H. and Welch, J. E.. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces. Physics of Fluids, 8, 2181–2189, 1965.
Phillips, T. N. and Williams, A. J.. Comparison of creeping and inertial flow of an Oldroyd-B fluid through planar and axisymmetric contractions. Journal of Non-Newtonian Fluid Mechanics, 108, 25–47, 2002.
Mompean, G. and Deville, M.. Unsteady finite volume simulation of Oldroyd-B fluid through a three-dimensional planar contraction. Journal of Non-Newtonian Fluid Mechanics, 872, 253–279, 1997.
Al Moatassime, H. and Jouron, C.. A multigrid method for solving steady viscoelastic fluid flow. Computer Methods in Applied Mechanics and Engineering, 190(31), 4061–4080, 2001.
Sasmal, G. P.. A finite volume approach for calculation of viscoelastic flow through an abrupt axisymmetric contraction. Journal of Non-Newtonian Fluid Mechanics, 56(1), 15–47, 1995.
Xia, H., Tucker, P. G., and Dawes, W. N.. Level sets for CFD in aerospace engineering. Progress in Aerospace Sciences, 46, 274–283, 2010.
Verstappen, R. W. C. P. and Veldman, A. E. P.. Symmetry-preserving discretization of turbulent flow. Journal of Computational Physics, 187, 343–368, 2003.
van der Plas, P., van der Heiden, H. J. L., Veldman, A. E. P., Luppes, R., and Verstappen, R. W. C. P.. Efficiently simulating viscous flow effects by means of regularization turbulence modeling and local grid refinement. Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Hawaii, paper ICCFD-2503, 2012.
Puzikova, V. and Marchevsky, I.. Application of the LS-STAG immersed boundary method for numerical simulation in coupled aeroelastic problems. Proceedings of the 11th World Congress on ComputationalMechanics (WCCMXI), Oñate, E., Oliver, J. and Huerta, A. (Eds), 20-25 July 2014, Barcelona, Spain., 2014.
Puzikova, V. and Marchevsky, I.. Extension of the LS-STAG cut-cell immersed boundary method for RANS-based turbulence models. Proceedings of the International Summer School-Conference “Advanced Problems in Mechanics”, June 30-July 5, St. Petersburg, Russia., 2014.
Saramito, P.. Efficient simulation of nonlinear viscoelastic fluid flows. Journal of Non-Newtonian Fluid Mechanics, 60(2-3), 199–223, 1995.
Alves, M. A., Oliveira, P. J., and Pinho, F. T.. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions. Journal of Non-Newtonian Fluid Mechanics, 110, 45–75, 2003.
Edussuriya, S. S., Williams, A. J., and Bailey, C.. A cell-centred finite volume method for modelling viscoelastic flow. Journal of Non-Newtonian Fluid Mechanics, 117, 47–61, 2004.
Li, X., Han, X., and Wang, X.. Numerical modeling of viscoelastic flows using equal low-order finite elements. Computer Methods in Applied Mechanics and Engineering, 199(9-12), 570–581, 2010.
Azaiez, J., Guénette, R., and Aït-Kadi, A.. Entry flow calculations using multi-mode models. Journal of Non-Newtonian Fluid Mechanics, 66, 271–281, 1996.
Aboubacar, M. and Webster, M. F.. A cell-vertex finite volume/element method on triangles for abrupt contraction viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, 98, 83–106, 2001.
Orlanski, I.. A simple boundary condition for unbounded hyperbolic flows. Journal of Computational Physics, 21, 251–269, 1976.
Dieci, L. and Eirola, T.. Positive definiteness in the numerical solution of Riccati differential equations. Numerische Mathematik, 67, 303–313, 1994.