An overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems. The overset grid approach alleviates some of the computational geometry difficulties traditionally associated with Arbitrary-Lagrangian-Eulerian (ALE) based, moving mesh methods for FSI. Our partitioned solution algorithm uses separate solvers for the fluid (finite volume method) and the structure (finite element method), with mesh motion computed only on a subset of component grids of our overset grid assembly. Our results indicate a significant reduction in computational cost for the mesh motion, and element quality is improved. Numerical studies of the benchmark test demonstrate the benefits of our overset mesh method over traditional approaches.
Noack, R. (2005) SUGGAR: A General Capability for Moving Body Overset Grid Assembly. Proceedings of the 17th AIAA Computational Fluid Dynamics Conference, Toronto, 6-9 June 2005, 1-21. http://dx.doi.org/10.2514/6.2005-5117
Noack, R.W. and Boger, D.A. (2009) Improvements to Suggar and Dirtlib for Overset Store Separation Simulations. Proceedings of the 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, 5-8 January 2009, 1-23.
Turek, S. and Hron, J. (2006) Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow. In: Fluid-Structure Interaction, Springer, Berlin, 371-385.
Dunne, T. and Rannacher, R. (2006) Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation. In: Fluid-Structure Interaction, Springer, Berlin, 110-145.
Dunne, T. (2006) An Eulerian Approach to Fluid-Structure Interaction and Goal-Oriented Mesh Adaptation. International Journal for Numerical Methods in Fluids, 51, 1017-1039. http://dx.doi.org/10.1002/fld.1205
Dunne, Th., Rannacher, R. and Richter, Th. (2010) Numerical Simulation of Fluid-Structure Interaction Based on Monolithic Variational Formulations. In: Numerical Fluid Structure Interaction, Contemporary Challenges in Mathematical Fluid Mechanics, World Scientific, Singapore.
Richter, Th. and Wick, Th. (2010) Finite Elements for Fluid-Structure Interaction in ALE and Fully Eulerian Coordinates. Computer Methods in Applied Mechanics and Engineering, 199, 2633-2642. http://dx.doi.org/10.1016/j.cma.2010.04.016
Rannacher, R. and Richter, T. (2010) An Adaptive Finite Element Method for Fluid-Structure Interaction Problems Based on a Fully Eulerian Formulation. In: Fluid Structure Interaction II, Springer, Berlin, 159-191.
Richter, T. (2013) A Fully Eulerian Formulation for Fluid-Structure-Interaction Problems. Journal of Computational Physics, 233, 227-240. http://dx.doi.org/10.1016/j.jcp.2012.08.047
Gerstenberger, A. and Wall, W.A. (2008) Enhancement of Fixed-Grid Methods towards Complex Fluid-Structure Interaction Applications. International Journal for Numerical Methods in Fluids, 57, 1227-1248. http://dx.doi.org/10.1002/fld.1782
Wall, W.A., Gerstenberger, A., Gamnitzer, P., Forster, C. and Ramm, E. (2006) Large Deformation Fluid-Structure Interaction-Advances in ALE Methods and New Fixed Grid Approaches. In: Bungartz, H.J. and Schafer, M., Eds., Fluid-Structure Interaction, Lecture Notes in Computational Science and Engineering, Springer, Berlin, 195-232.
Wall, W.A., Gamnitzer, P. and Gerstenberger, A. (2008) Fluid-Structure Interaction Approaches on Fixed Grids Based on Two Different Domain Decomposition Ideas. International Journal of Computational Fluid Dynamics, 22, 411-427. http://dx.doi.org/10.1080/10618560802208567
Wall, W.A., Gerstenberger, A. and Mayer, U.M. (2009) Advances in Fixed-Grid Fluid Structure Interaction. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A. and Périaux, J., Eds., ECCOMAS Multidisciplinary Jubilee Symposium in Computational Methods in Applied Sciences, Springer, Berlin, 235-249. http://dx.doi.org/10.1007/978-1-4020-9231-2_16
Lv, X., Zhao, Y., Huang, X.Y., Xia, G.H. and Su, X.H. (2007) A Matrix-Free Implicit Unstructured Multigrid Finite Volume Method for Simulating Structural Dynamics and Fluid-Structure Interaction. Journal of Computational Physics, 225, 120-144. http://dx.doi.org/10.1016/j.jcp.2006.11.023
Boffi, D., Gastaldi, L., Heltai, L. and Peskin, C.S. (2008) On the Hyper-Elastic Formulation of the Immersed Boundary Method. Computer Methods in Applied Mechanics and Engineering, 197, 2210-2231.
Borazjani, I., Ge, L. and Sotiropoulos, F. (2008) Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies. Journal of Computational Physics, 227, 7587-7620. http://dx.doi.org/10.1016/j.jcp.2008.04.028
Borazjani, I. (2013) Fluid-Structure Interaction, Immersed Boundary-Finite Element Method Simulations of Bio-Prosthetic Heart Valves. Computer Methods in Applied Mechanics and Engineering, 257, 103-116. http://dx.doi.org/10.1016/j.cma.2013.01.010
Zhu, L.D. and Peskin, C.S. (2002) Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method. Journal of Computational Physics, 179, 452-468. http://dx.doi.org/10.1006/jcph.2002.7066
Wang, H., Chessa, J., Liu, W.K. and Belytschko, T. (2008) The Immersed/Fictitious Element Method for Fluid-Structure Interaction: Volumetric Consistency, Compressibility and Thin Members. International Journal for Numerical Methods in Engineering, 74, 32-55. http://dx.doi.org/10.1002/nme.2153
Baaijens, F.P.T. (2001) A Fictitious Domain/Mortar Element Method for Fluid-Structure Interaction. International Journal for Numerical Methods in Fluids, 35, 743-761. http://dx.doi.org/10.1002/1097-0363(20010415)35:7 3.0.CO;2-A
De Hart, J., Peters, G.W.M., Schreurs, P.J.G. and Baaijens, F.P.T. (2003) A Three-Dimensional Computational Analysis of Fluid-Structure Interaction in the Aortic Valve. Journal of Biomechanics, 36, 103-112. http://dx.doi.org/10.1016/S0021-9290(02)00244-0
Swim, E.W. and Seshaiyer, P. (2006) A Nonconforming Finite Element Method for Fluid-Structure Interaction Problems. Computer Methods in Applied Mechanics and Engineering, 195, 2088-2099. http://dx.doi.org/10.1016/j.cma.2005.01.017
Mayer, U.M., Gerstenberger, A. and Wall, W.A. (2009) Interface Handling for Three-Dimensional Higher-Order XFEM-Computations in Fluid-Structure Interaction. International Journal for Numerical Methods in Engineering, 79, 846-869. http://dx.doi.org/10.1002/nme.2600
Mayer, U.M., Popp, A., Gerstenberger, A. and Wall, W.A. (2010) 3D Fluid-Structure-Contact Interaction Based on a Combined XFEM FSI and Dual Mortar Contact Approach. Computational Mechanics, 46, 53-67. http://dx.doi.org/10.1007/s00466-010-0486-0
Shahmiri, S., Gerstenberger, A. and Wall, W.A. (2011) An XFEM-Based Embedding Mesh Technique for Incompressible Viscous Flows. International Journal for Numerical Methods in Fluids, 65, 166-190. http://dx.doi.org/10.1002/fld.2471
Cottet, G.H. and Maitre, E. (2006) A Level Set Method for Fluid-Structure Interactions with Immersed Surfaces. Mathematical Models and Methods in Applied Sciences, 16, 415-438. http://dx.doi.org/10.1142/S0218202506001212
Cottet, G.H., Maitre, E. and Milcent, T. (2008) Eulerian Formulation and Level Set Models for Incompressible Fluid-Structure Interaction. ESAIM: Mathematical Modelling and Numerical Analysis, 42, 471-492. http://dx.doi.org/10.1051/m2an:2008013
Legay, A., Chessa, J. and Belytschko, T. (2006) An Eulerian-Lagrangian Method for Fluid-Structure Interaction Based on Level Sets. Computer Methods in Applied Mechanics and Engineering, 195, 2070-2087. http://dx.doi.org/10.1016/j.cma.2005.02.025
Antoci, C., Gallati, M. and Sibilla, S. (2007) Numerical Simulation of Fluid-Structure Interaction by SPH. Computers & Structures, 85, 879-890. http://dx.doi.org/10.1016/j.compstruc.2007.01.002
Rabczuk, T., Gracie, R., Song, J.H. and Belytschko, T. (2010) Immersed Particle Method for Fluid-Structure Interaction. International Journal for Numerical Methods in Engineering, 81, 48-71.
Caleyron, F., Combescure, A., Faucher, V. and Potapov, S. (2013) SPH Modeling of Fluid-Solid Interaction for Dynamic Failure Analysis of Fluid-Filled Thin Shells. Journal of Fluids and Structures, 39, 126-153. http://dx.doi.org/10.1016/j.jfluidstructs.2013.02.023
Idelsohn, S.R., Onate, E. and Del Pin, F. (2003) A Lagrangian Meshless Finite Element Method Applied to Fluid-Structure Interaction Problems. Computers & Structures, 81, 655-671. http://dx.doi.org/10.1016/S0045-7949(02)00477-7
Idelsohn, S.R., Onate, E., Del Pin, F. and Calvo, N. (2006) Fluid-Structure Interaction Using the Particle Finite Element Method. Computer Methods in Applied Mechanics and Engineering, 195, 2100-2123. http://dx.doi.org/10.1016/j.cma.2005.02.026
Hirt, C.W., Amsden, A.A. and Cook, J.L. (1974) An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds. Journal of Computational Physics, 14, 227-253. http://dx.doi.org/10.1016/0021-9991(74)90051-5
Donea, J., Giuliani, S. and Halleux, J.P. (1982) An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions. Computer Methods in Applied Mechanics and Engineering, 33, 689-723. http://dx.doi.org/10.1016/0045-7825(82)90128-1
Belytschko, T.B. and Kennedy, J.M. (1978) Computer Models for Subassembly Simulation. Nuclear Engineering and Design, 49, 17-38. http://dx.doi.org/10.1016/0029-5493(78)90049-3
Belytschko, T., Flanagan, D.P. and Kennedy, J.M. (1982) Finite Element Methods with User-Controlled Meshes for Fluid-Structure Interaction. Computer Methods in Applied Mechanics and Engineering, 33, 669-688.
Hughes, T.J.R., Liu, W.K. and Zimmermann, T.K. (1981) Lagrangian-Eulerian Finite Element Formulation for Incompressible Viscous Flows. Computer Methods in Applied Mechanics and Engineering, 29, 329-249. http://dx.doi.org/10.1016/0045-7825(81)90049-9
Donea, J., Huerta, A., Ponthot, J.Ph. and Rodríguez-Ferran, A. (2004) Arbitrary Lagrangian-Eulerian Methods, Chapter 14. John Wiley & Sons, Ltd., Hoboken.
Tezduyar, T.E., Sathe, S., Pausewang, J., Schwaab, M., Christopher, J. and Crabtree, J. (2008) Interface Projection Techniques for Fluid-Structure Interaction Modeling with Moving-Mesh Methods. Computational Mechanics, 43, 39-49. http://dx.doi.org/10.1007/s00466-008-0261-7
Le Tallec, P. and Mouro, J. (2001) Fluid-Structure Interaction with Large Structural Displacements. Computer Methods in Applied Mechanics and Engineering, 190, 3039-3067.
Wall, W.A., Genkinger, S. and Ramm, E. (2007) A Strong Coupling Partitioned Approach for Fluid-Structure Interaction with Free Surfaces. Computers & Fluids, 36, 169-183. http://dx.doi.org/10.1016/j.compfluid.2005.08.007
Degroote, J., Bathe, K.J. and Vierendeels, J. (2009) Performance of a New Partitioned Procedure versus a Monolithic Procedure in Fluid-Structure Interaction. Computers & Structures, 87, 793-801. http://dx.doi.org/10.1016/j.compstruc.2008.11.013
Sonntag, S.J., Kaufmann, T.A.S., Büsen, M.R., Laumen, M., Linde, T., Schmitz-Rode, T. and Steinseifer, U. (2013) Simulation of a Pulsatile Total Artificial Heart: Development of a Partitioned Fluid Structure Interaction Model. Journal of Fluids and Structures, 38, 187-204. http://dx.doi.org/10.1016/j.jfluidstructs.2012.11.011
Habchi, C., Russeil, S., Bougeard, D., Harion, J.L., Lemenand, T., Ghanem, A., Della Valle, D. and Peerhossaini, H. (2013) Partitioned Solver for Strongly Coupled Fluid-Structure Interaction. Computers & Fluids, 71, 306-319.
Jog, C.S. and Pal, R.K. (2011) A Monolithic Strategy for Fluid-Structure Interaction Problems. International Journal for Numerical Methods in Engineering, 85, 429-460. http://dx.doi.org/10.1002/nme.2976
Quaini, A., Canic, S., Glowinski, R., Igo, S., Hartley, C.J., Zoghbi, W. and Little, S. (2012) Validation of a 3D Computational Fluid-Structure Interaction Model Simulating Flow through an Elastic Aperture. Journal of Biomechanics, 45, 310-318. http://dx.doi.org/10.1016/j.jbiomech.2011.10.020
Hubner, B., Walhorn, E. and Dinkler, D. (2004) A Monolithic Approach to Fluid-Structure Interaction Using Space-Time Finite Elements. Computer Methods in Applied Mechanics and Engineering, 193, 2087-2104. http://dx.doi.org/10.1016/j.cma.2004.01.024
Pena, G. and Prud’homme, C. (2010) Construction of a High Order Fluid-Structure Interaction Solver. Journal of Computational and Applied Mathematics, 234, 2358-2365. http://dx.doi.org/10.1016/j.cam.2009.08.093
Tezduyar, T.E., Takizawa, K., Moorman, C., Wright, S. and Christopher, J. (2010) Space-Time Finite Element Computation of Complex Fluid-Structure Interactions. International Journal for Numerical Methods in Fluids, 64, 1201-1218. http://dx.doi.org/10.1002/fld.2221
Persson, P.O., Bonet, J. and Peraire, J. (2009) Discontinuous Galerkin Solution of the Navier-Stokes Equations on Deformable Domains. Computer Methods in Applied Mechanics and Engineering, 198, 1585-1595. http://dx.doi.org/10.1016/j.cma.2009.01.012
Wang, H. and Belytschko, T. (2009) Fluid-Structure Interaction by the Discontinuous-Galerkin Method for Large Deformations. International Journal for Numerical Methods in Engineering, 77, 30-49. http://dx.doi.org/10.1002/nme.2396
Bazilevs, Y., Calo, V.M., Zhang, Y. and Hughes, T.J.R. (2006) Isogeometric Fluid-Structure Interaction Analysis with Applications to Arterial Blood Flow. Computational Mechanics, 38, 310-322. http://dx.doi.org/10.1007/s00466-006-0084-3
Bazilevs, Y., Calo, V.M., Hughes, T.J.R. and Zhang, Y. (2008) Isogeometric Fluid-Structure Interaction: Theory, Algorithms, and Computations. Computational Mechanics, 43, 3-37. http://dx.doi.org/10.1007/s00466-008-0315-x
Bazilevs, Y., Hsu, M.C., Kiendl, J., Wüchner, R. and Bletzinger, K.U. (2011) 3D Simulation of Wind Turbine Rotors at Full Scale. Part II: Fluid-Structure Interaction Modeling with Composite Blades. International Journal for Numerical Methods in Fluids, 65, 236-253. http://dx.doi.org/10.1002/fld.2454
Stein, K., Tezduyar, T. and Benney, R. (2003) Mesh Moving Techniques for Fluid-Structure Interactions with Large Displacements. Journal of Applied Mechanics, 70, 58-63. http://dx.doi.org/10.1115/1.1530635
Stein, K., Tezduyar, T.E. and Benney, R. (2004) Automatic Mesh Update with the Solid-Extension Mesh Moving Technique. Computer Methods in Applied Mechanics and Engineering, 193, 2019-2032.
Tezduyar, T.E. (2001) Finite Element Methods for Flow Problems with Moving Boundaries and Interfaces. Archives of Computational Methods in Engineering, 8, 83-130. http://dx.doi.org/10.1007/BF02897870
Tezduyar, T.E., Sathe, S., Keedy, R. and Stein, K. (2006) Space-Time Finite Element Techniques for Computation of Fluid-Structure Interactions. Computer Methods in Applied Mechanics and Engineering, 195, 2002-2027. http://dx.doi.org/10.1016/j.cma.2004.09.014
Tezduyar, T.E., Sathe, S. and Stein, K. (2006) Solution Techniques for the Fully Discretized Equations in Computation of Fluid-Structure Interactions with the Space-Time Formulations. Computer Methods in Applied Mechanics and Engineering, 195, 5743-5753.
Tezduyar, T.E. and Sathe, S. (2007) Modelling of Fluid-Structure Interactions with the space-Time Finite Elements: Solution Techniques. International Journal for Numerical Methods in Fluids, 54, 855-900. http://dx.doi.org/10.1002/fld.1430
Tezduyar, T.E., Sathe, S., Schwaab, M. and Conklin, B.S. (2008) Arterial Fluid Mechanics Modeling with the Stabilized Space-Time Fluid-Structure Interaction Technique. International Journal for Numerical Methods in Fluids, 57, 601-629. http://dx.doi.org/10.1002/fld.1633
Torii, R., Oshima, M., Kobayashi, T., Takagi, K. and Tezduyar, T.E. (2006) Computer Modeling of Cardiovascular Fluid-Structure Interactions with the Deforming-Spatial-Domain/Stabilized Space-Time Formulation. Computer Methods in Applied Mechanics and Engineering, 195, 1885-1895. http://dx.doi.org/10.1016/j.cma.2005.05.050
Gamnitzer, P. and Wall, W.A. (2006) An ALE-Chimera Method for Large Deformation Fluid Structure Interaction. European Conference on Computational Fluid Dynamics (ECCOMAS CFD), TU Deflt, 5-8 September 2006, 1-14.
Gordnier, R.E. and Melville, R.B. (2000) Transonic Flutter Simulations Using an Implicit Aeroelastic Solver. Journal of Aircraft, 37, 872-879. http://dx.doi.org/10.2514/2.2683
Ahmad, J. and Duque, E.P. (1996) Helicopter Rotor Blade Computation in Unsteady Flows Using Moving Overset Grids. Journal of Aircraft, 33, 54-60. http://dx.doi.org/10.2514/3.46902
Hierholz, K.H. and Wagner, S. (1998) Simulation of Fluid-Structure Interaction at the Helicopter Rotor. 21st ICAS Congress, Melbourne.
Carrica, P.M., Huang, J., Noack, R., Kaushik, D., Smith, B. and Stern, F. (2010) Large-Scale DES Computations of the Forward Speed Diffraction and Pitch and Heave Problems for a Surface Combatant. Computers & Fluids, 39, 1095-1111. http://dx.doi.org/10.1016/j.compfluid.2010.02.002
Freitas, C.J. and Runnels, S.R. (1999) Simulation of Fluid-Structure Interaction Using Patched-Overset Grids. Journal of Fluids and Structures, 13, 191-207. http://dx.doi.org/10.1006/jfls.1998.0200
Ikegawa, M., Kaiho, M. and Kato, C. (1994) FEM/FDM Composite Scheme for Viscous Incompressible Flow Analysis. Computer Methods in Applied Mechanics and Engineering, 112, 149-163.
Kaiho, M., Ikegawa, M. and Kato, C. (1997) Parallel Overlapping Scheme for Viscous Incompressible Flows. International Journal for Numerical Methods in Fluids, 24, 1341-1352. http://dx.doi.org/10.1002/(SICI)1097-0363(199706)24:12 3.0.CO;2-G
Kato, C., Kaiho, M. and Manabe, A. (2003) An Overset Finite-Element Large-Eddy Simulation Method with Applications to Turbomachinery and Aeroacoustics: Flow Simulation and Modeling. Journal of Applied Mechanics, 70, 32-43. http://dx.doi.org/10.1115/1.1530637
Frey, P. and George, P.L. (2010) Mesh Generation. Wiley-ISTE, New York.
Wick, T. (2011) Fluid-Structure Interactions Using Different Mesh Motion Techniques. Computers & Structures, 89, 1456-1467.
Campbell, R.L. and Paterson, E.G. (2011) Fluid-Structure Interaction Analysis of Flexible Turbomachinery. Journal of Fluids and Structures, 27, 1376-1391. http://dx.doi.org/10.1016/j.jfluidstructs.2011.08.010
Lesoinne, M. and Farhat, C. (1996) Geometric Conservation Laws for Flow Problems with Moving Boundaries and Deformable Meshes, and Their Impact on Aeroelastic Computations. Computer Methods in Applied Mechanics and Engineering, 134, 71-90.
Farhat, C., Geuzaine, P. and Grandmont, C. (2001) The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids. Journal of Computational Physics, 174, 669-694. http://dx.doi.org/10.1006/jcph.2001.6932
Kamakoti, R. and Shyy, W. (2004) Fluid-Structure Interaction for Aeroelastic Applications. Progress in Aerospace Sciences, 40, 535-558. http://dx.doi.org/10.1016/j.paerosci.2005.01.001
Slone, A.K., Pericleous, K., Bailey, C. and Cross, M. (2002) Dynamic Fluid-Structure Interaction Using Finite Volume Unstructured Mesh Procedures. Computers and Structures, 80, 371-390. http://dx.doi.org/10.1016/S0045-7949(01)00177-8
Thomas, P.D. and Lombard, C.K. (1979) Geometric Conservation Law and Its Application to Flow Computations on Moving Grids. AIAA Journal, 17, 1030-1037. http://dx.doi.org/10.2514/3.61273
Gurtin, M.E., Fried, E. and Anand, L. (2009) The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge.
Yigit, S., Schafer, M. and Heck, M. (2008) Grid Movement Techniques and Their Influence on Laminar Fluid-Structure Interaction Computations. Journal of Fluids and Structures, 24, 819-832. http://dx.doi.org/10.1016/j.jfluidstructs.2007.12.002
Zhang, H., Zhang, X.L., Ji, S.H., Guo, Y.H., Ledezma, G., Elabbasi, N. and deCougny, H. (2003) Recent Development of Fluid-Structure Interaction Capabilities in the ADINA System. Computers & Structures, 81, 1071-1085. http://dx.doi.org/10.1016/S0045-7949(03)00009-9
Boger, D.A., Noack, R.W. and Paterson, E.G. (2010) FoamedOver: A Library to Add a Dynamic Overset Grid Capability to OpenFOAM. 5th Open-FOAM Workshop, Chalmers University of Technology, Gothenburg, 21-24 June 2010, 24.
Weller, H.G., Tabor, G., Jasak, H. and Fureby, C. (1998) A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques. Computers in Physics, 12, 620. http://dx.doi.org/10.1063/1.168744
Jasak, H., Jemcov, A. and Tukovic, Z. (2007) OpenFOAM: A C++ Library for Complex Physics Simulations. International Workshop on Coupled Methods in Numerical Dynamics, IUC, Dubrovnik, 19-21 September 2007, 1-20.
Jasak, H. and Rusche, H. (2009) Dynamic Mesh Handling in OpenFOAM. Proceeding of the 47th Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, 5-8 January 2009, 1-10. http://dx.doi.org/10.2514/6.2009-341
Jasak, H. and Tukovic, Z. (2010) Dynamic Mesh Handling in OpenFOAM Applied to Fluid-Structure Interaction Simulations. Proceedings of the V European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010), Lisbon, 14-17 June 2010.
Issa, R.I. (1986) Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting. Journal of Computational Physics, 62, 40-65. http://dx.doi.org/10.1016/0021-9991(86)90099-9
Issa, R.I., Gosman, A.D. and Watkins, A.P. (1986) The Computation of Compressible and Incompressible Recirculating Flows by a Non-Iterative Implicit Scheme. Journal of Computational Physics, 62, 66-82. http://dx.doi.org/10.1016/0021-9991(86)90100-2
Bathe, K.J. (1996) Finite Element Procedures. Klaus-Jurgen Bathe, Englewood Cliffs, New Jersey.
Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2001) Concepts and Applications of Finite Element Analysis. 4 Edition, John Wiley & Sons, Hoboken.
Crisfield, M.A. (1991) Non-Linear Finite Element Analysis of Solids and Structures. John Wiley & Sons Inc., Hoboken.
Hughes, T.J.R. (1987) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ.
Noack, R.W. (2005) DiRTlib: A Library to Add an Overset Capability to Your Flow Solver. Proceedings of the 17th Annual AIAA Computational Fluid Dynamics Conference, Toronto, 6-9 June 2005, 1-20. http://dx.doi.org/10.2514/6.2005-5116
Noack, R.W. (2007) A Direct Cut Approach for Overset Hole Cutting. Proceedings of the 18th AIAA Computational Fluid Dynamics Conference, Miami, 25-28 June 2007, 1-30. http://dx.doi.org/10.2514/6.2007-3835
Noack, R.W., Boger, D.A., Kunz, R.F. and Carrica, P.M. (2009) Suggar++: An Improved General Overset Grid Assembly Capability. Proceedings of the 47th AIAA Aerospace Science and Exhibit, 22-25 June 2009, San Antonio, 1-48.
Noack, R.W. (2011) Unstructured Mixed Element Mesh Refinement Using Templates Generated by Metaprogramming. Proceedings of the 20th AIAA Computational Fluid Dynamics Conference, Honolulu, 27-30 June 2011, 1-32. http://dx.doi.org/10.2514/6.2011-3054
Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F. and Zhang, H. (2012) PETSc Web Page, 2012.
Suhs, N.E., Rogers, S.E., Dietz, W.E. and Kwak, D. (2002) PEGASUS 5: An Automated Pre-Processor for Overset-Grid CFD. AIAA Journal, 41, 1037-1045.
Kunz, R.F., Siebert, B.W., Cope, W.K., Foster, N.F., Antal, S.P. and Ettorre, S.M. (1998) A Coupled Phasic Exchange Algorithm for Three-Dimensional Multi-Field Analysis of Heated Flows with Mass Transfer. Computers & Fluids, 27, 741-768. http://dx.doi.org/10.1016/S0045-7930(97)00064-9
Ramm, E. and Wall, W.A. (1998) Fluid-Structure Interaction Based upon a Stabilized (ALE) Finite Element Method. 4th World Congress on Computational Mechanics: New Trends and Applications, CIMNE, Barcelona, 1998, 1-20.