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Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction

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Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems

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References

  1. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.

    Google Scholar 

  2. M. Lesieur, Turbulence in Fluids, Kluwer, Dordrecht, 1990.

    Google Scholar 

  3. E. Guyon, J.P. Hulin, and L. Petit, Hydrodynamique Physique, Intereditions/Editions du CNRS, Paris, 1991.

    Google Scholar 

  4. R. Glowinski, Finite element methods for incompressible viscous flow, in Handbook of Numerical Analysis, Vol. IX, P.G. Ciarlet, J.-L. Lions eds., North-Holland, Amsterdam, 2003, 3–1176.

    Google Scholar 

  5. W. Prager, Introduction to Mechanics of Continua, Ginn and Company, Boston, MA, 1961.

    Google Scholar 

  6. G.K. Batchelor, An Introduction to Fluid Mechanics, Cambridge University Press, Cambridge, U.K., 1967.

    Google Scholar 

  7. A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 1990.

    Google Scholar 

  8. R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York, 1984.

    Google Scholar 

  9. M.O. Bristeau, R. Glowinski, B. Mantel, J. Periaux, P. Perrier, Numerical Methods for incompressible and compressible Navier-Stokes problems, in Finite Element in Fluids, Vol. 6, R.H. Gallagher, G. Carey, J.T. Oden, and O.C. Zienkiewicz eds., J. Wiley, Chicester, 1985, 1–40.

    Google Scholar 

  10. O. Pironneau, Finite Element Methods for Fluids, J. Wiley, Chicester, 1989.

    Google Scholar 

  11. J. Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Mathematica, 63 (1934), 193–248.

    MATH  Google Scholar 

  12. J. Leray, Essai sur les mouvements d’un liquide visqueux que limitent des parois, J. Math. Pures et Appl., 13 (1934), 331–418.

    MATH  Google Scholar 

  13. E. Hopf, Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen, Math. Nachrichten, 4 (1951), 213–231.

    MathSciNet  MATH  Google Scholar 

  14. J. Leray, Aspects de la mécanique théorique des fluides, La Vie des Sciences, Comptes Rendus de l’Académie des Sciences, Paris, Série Générale, 11 (1994), 287–290.

    Google Scholar 

  15. J.L. Lions and G. Prodi, Un théorème d’existence et d’unicité dans les équations de Navier-Stokes en dimension 2, C.R. Acad. Sci., Paris 248, 3519–3521.

    Google Scholar 

  16. J.L. Lions, Equations Différentielles Opérationnelles et Problèmes aux Limites, Springer-Verlag, Berlin, 1961.

    Google Scholar 

  17. J.L. Lions, Quelques Méthodes de Résolution des Problémes aux Limites Non Linéaires, Dunod, Paris, 1969.

    Google Scholar 

  18. O. Ladysenskaya, Theory and Numerical Analysis of the Navier-Stokes Equations, Gordon and Breach, New York, NY, 1969.

    Google Scholar 

  19. R. Temam, The Mathematical Theory of Viscous Incompressible Flow, North-Holland, Amsterdam, 1977.

    Google Scholar 

  20. L. Tartar, Topics in Nonlinear Analysis, Publications Mathématiques d’Orsay, Université Paris-Sud, Départment de Mathématiques, Paris, 1978.

    Google Scholar 

  21. H.O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, Boston, MA, 1989.

    Google Scholar 

  22. P.L. Lions, Mahtematical Topics in Fluid Mechanics, Vol I: Incompressible Models, Oxford University, Oxford, UK, 1996.

    Google Scholar 

  23. M. Marion and R. Temam, Navier-Stokes Equations, in Handbook of Numerical Analysis, Vol. VI, P.G. Ciarlet, J.-L. Lions eds., North-Holland, Amsterdam, 1998, 503–689.

    Google Scholar 

  24. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.

    Google Scholar 

  25. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, NY, 1991.

    Google Scholar 

  26. S.C. Brenner and L.R. Scott The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, NY, 1994.

    Google Scholar 

  27. N.N. Yanenko, The Method of Fractional Steps, Springer-Verlag, Berlin, 1971.

    Google Scholar 

  28. G.I. Marchuk, Methods of Numerical Mathematics, Springer-Verlag, New York, NY, 1975.

    Google Scholar 

  29. G.I. Marchuk, Splitting and alternating direction methods. In Ciarlet, P.G., and Lions, J.L. (eds.) Handbook of Numerical Analysis, Vol I, North-Holland, Amsterdam, 1990, 197–462.

    Google Scholar 

  30. M. Crouzeix and A. Mignot, Analyse Numérique des Equations Différentielles Ordiuaires, Masson, Paris, 1984.

    Google Scholar 

  31. R. Glowinski and P. Le Tallec, Augmented Lagrangians and Operator Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989.

    Google Scholar 

  32. R. Glowinski, Viscous flow simulation by finite element methods and related numerical techniques. In Murman, E.M., and Abarbanel, S.S. (eds.) Progress and Supercomputing in Computational Fluid Dynamics, Birkhauser, Boston, MA, 1985, 173–210.

    Google Scholar 

  33. R. Glowinski, Splitting methods for the numerical solution of the incompressible Navier-Stokes equations. In Balakrishnan, A.V., Dorodnitsyn, A.A., and Lions, J.L. (eds.) Vistas in Applied Mathematics, Optimization Software, New York, NY, 1986, 57–95.

    Google Scholar 

  34. G. Strang, On the construction and comparison of difference schemes, SIAM J. Num. Anal., 5 (1968), 506–517.

    MathSciNet  MATH  Google Scholar 

  35. J.T. Beale and A. Majda, Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp., 37 (1981), 243–260.

    MathSciNet  Google Scholar 

  36. R. Leveque and J. Oliger, Numerical methods based on additive splitting for hyperbolic partial differential equations, Math. Comp., 37 (1983), 243–260.

    MathSciNet  Google Scholar 

  37. P.A. Raviart and J.M. Thomas, Introduction à l’ Analyse Numérique des Equations aux Dérivées Partielles, Masson, Paris, 1983.

    Google Scholar 

  38. A.J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comp. Phys., 2 (1967), 12–26.

    MATH  Google Scholar 

  39. A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp., 23 (1968), 341–354.

    MathSciNet  Google Scholar 

  40. R. Temam, Sur l’approximation deséquations de Navier-Stokes par la méthode des pas fractionnaires (I), Arch. Rat. Mech. Anal., 32 (1969), 135–153.

    MathSciNet  MATH  Google Scholar 

  41. R. Temam, Sur l’approximation deséquations de Navier-Stokes par la méthode des pas fractionnaires (II), Arch. Rat. Mech. Anal., 33 (1969), 377–385.

    MathSciNet  MATH  Google Scholar 

  42. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994.

    Google Scholar 

  43. J. Daniel, The Approximate Minimization of Functionals, Prentice Hall, Englewood Cliffs, NJ, 1970.

    Google Scholar 

  44. E. Polak, Computational Methods in Optimization, Academic Press, New York, NY, 1971.

    Google Scholar 

  45. M.R. Hestenes and E.L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Bureau National Standards, Section B, 49 (1952), 409–436.

    MathSciNet  Google Scholar 

  46. R.W. Freund, G.H. Golub, and N.M. Nachtigal, Iterative solution of linear systems, Acta Numerica 1992, Cambridge University Press, 1992, 57–100.

    Google Scholar 

  47. J. Nocedal, Theory of algorithms for unconstrained optimization, Acta Numerica 1992, Cambridge University Press, 1992, 199–242.

    Google Scholar 

  48. C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, PA, 1995.

    Google Scholar 

  49. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, Boston, MA, 1995.

    Google Scholar 

  50. G.H. Golub and D.P. O’Leary, Some history of the conjugate gradient and Lanczos algorithms: 1948-1976, SIAM Review, 31 (1989), 50–102.

    Article  MathSciNet  Google Scholar 

  51. E. Zeidler, Nonlinear Functional Analysis and its Applications. Volume I: Fixed-Point Theorems, Springer-Verlag, New York, NY, 1986.

    Google Scholar 

  52. I. Ekeland and R. Teman, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.

    Google Scholar 

  53. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, 1970.

    Google Scholar 

  54. J.M. Ortega, and W.C. Rheinboldt, Local and global convergence of generalized linear iterations. In Ortega, J.M., and Rheinboldt, W.C. (eds.) Numerical Solution of Nonlinear Problems, SIAM, Philadelphia, PA, 1970.

    Google Scholar 

  55. J.M. Ortega and W.C. Rheinboldt, A general convergence result for unconstrained minimization methods, SIAM J. Num. Anal., 9 (1972), 40–43.

    MathSciNet  Google Scholar 

  56. M. Avriel, Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, NJ, 1976.

    Google Scholar 

  57. M.J.D. Powell, Some convergence properties of the conjugate gradient method, Math. Program., 11 (1976), 42–49.

    Article  MathSciNet  MATH  Google Scholar 

  58. M.J.D. Powell, Restart procedures of the conjugate gradient method, Math. Program., 12 (1977), 148–162.

    Google Scholar 

  59. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  60. J.B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms, Springer-Verlag, Berlin, 1993.

    Google Scholar 

  61. M. Crouzeix, Etude d’une méthode de linéarisation. Résolution numérique des équations de Stokes stationaires. In Approximations et Méthodes Itératives de Résolution d’Inéquations Variationelles et de Problémes Non Linéaires, Cahiers de l’IRIA, 12, 1974, 139–244.

    Google Scholar 

  62. M. Crouzeix, On an operator related to the convergence of Uzawa’s algorithm for the Stokes equation. In Bristeau, M.O., Etgen, G., Fitzgibbon, W., Lions, J. L., Périaux, J., and Wheeler, M.F. (eds.) Computational Science for the 21st Century, Wiley, Chichester, 1997, 242–259.

    Google Scholar 

  63. J. Cahouet and J.P. Chabard, Some fast 3-D solvers for the generalized Stokes problem, Int. J. Numer. Meth. in Fluids, 8, 1988, 269–295.

    MathSciNet  Google Scholar 

  64. J.E. Dennis and R.B. Schnabel, A view of unconstrained optimization. In Newhauser, G.L., Rinnooy Kan, A.H.G., and Todd, M.J. (eds.) Handbook in Operations Research and Management Science, Vol. 1: Optimization, North-Holland, Amsterdam, 1989, 1–66.

    Google Scholar 

  65. F. Thomasset, Implementation of Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York, NY, 1981.

    Google Scholar 

  66. R. Peyret and T.D. Taylor, Computational Methods for Fluid Flow, Springer-Verlag, New York, NY, 1982.

    Google Scholar 

  67. C. Cuvelier, A. Segal, and A. Van Steenhoven, Finite Element Methods and Navier-Stokes Equations, Reidel, Dordrecht, 1986.

    Google Scholar 

  68. M. Fortin, Finite element solution of the Navier-Stokes equations, Acta Numerica 1993, Cambridge University Press, 1993, 239–284.

    Google Scholar 

  69. M.D. Gunzburger, Finite Element Methods for Viscous Incompressible Flows, Academic Press, Boston, MA, 1989.

    Google Scholar 

  70. C.A.J. Fletcher, Computational Techniques for Fluid Dynamics, Volume 1: Fundamental and General Techniques, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  71. C.A.J. Fletcher, Computational Techniques for Fluid Dynamics, Volume 2: Specific Techniques for Different Flow Categories, Springer-Verlag, Berlin, 1991.

    Google Scholar 

  72. M.D. Gunzburger and R.A. Nicolaides (eds.), Incompressible Computational Fluid Dynamics, Cambridge University Press, New York, NY, 1993.

    Google Scholar 

  73. L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations, Birkhauser, Basel, 1993.

    Google Scholar 

  74. F.K. Hebeker, R. Rannacher, and G. Wittum (eds.), Numerical Methods for the Navier-Stokes Equations, Vieweg, Braunschweig/Wiesbaden, 1994.

    Google Scholar 

  75. P.M. Gresho and R.L. SANI, Incompressible Flow and the Finite Element Method: Advection-Diffusion and Isothermal Laminar Flow, J. Wiley, Chichester, 1998.

    Google Scholar 

  76. E. Fernandez-Cara and M.M. Beltran, The convergence of two numerical schemes for the Navier-Stokes equations, Numerische Mathematik, 55 (1989), 33–60.

    Article  MathSciNet  Google Scholar 

  77. P. Kloucek and F.S. Rys, On the stability of the fractional step-¸-scheme for the Navier-Stokes equations, SIAM J. Num. Anal., 31 (1994), 1312–1335.

    MathSciNet  Google Scholar 

  78. P. Hood and C. Taylor, A numerical solution of the Navier-Stokes equations using the finite element technique, Computers and Fluids, 1 (1973), 73–100.

    MathSciNet  Google Scholar 

  79. M. Bercovier and O. Pironneau, Error estimates for finite element method solution of the Stokes problem in the primitive variables, Numer. Math., 33 (1979), 211–224.

    Article  MathSciNet  Google Scholar 

  80. G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, NJ, 1973.

    Google Scholar 

  81. P.G. Ciarlet, Basic error estimates for elliptic problems. In Ciarlet, P.G., and Lions, J.L. (eds.) Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam, 1991, 17–351.

    Google Scholar 

  82. R. Glowinski, Finite element methods for the numerical simulation of incompressible viscous flow. Introduction to the control of the Navier-Stokes equations. In Anderson, C.R., and Greengard, C. (eds.) Vortex Dynamics and Vortex Methods, Lecture in Applied Mathematics, Vol. 28, American Mathematical Society, Providence, RI, 1991, 219–301.

    Google Scholar 

  83. M.O. Bristeau, R. Glowinski, and J. Periaux, Numerical methods for the Navier-Stokes equations. Applications to the simulation of compressible and incompressible viscous flow, Computer Physics Reports, 6 (1987), 73–187.

    Article  Google Scholar 

  84. E.J. Dean, R. Glowinski, and C.H. Li, Supercomputer solution of partial differential equation problems in Computational Fluid Dynamics and in Control, Computer Physics Communications, 53 (1989), 401–439.

    Article  MathSciNet  Google Scholar 

  85. R. Glowinski and O. Pironneau, Finite element methods for Navier-Stokes equations, Annual Review of Fluid Mechanics, 24 (1992), 167–204.

    Article  MathSciNet  Google Scholar 

  86. T.J.R. Hughes, L.P. Franca, and M. Balestra, A new finite element formulation for Computational Fluid Dynamics: V. Circumventing the Babaska-Brezzi Condition; A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal-order interpolation, Comp. Meth. Appl. Mech. Eng., 59 (1986), 85–100.

    Article  MathSciNet  Google Scholar 

  87. J. Douglas and J. Wang, An absolutely stabilized finite element method for the Stokes problem, Math. Comp., 52 (1989), 495–508.

    MathSciNet  Google Scholar 

  88. Z. Cai and J. Douglas, An analytic basis for multigrid methods for stabilized finite element methods for the Stokes problem. In Bristeau, M.O., Etgen, G., Fitzgibbon, W., Lions, J.L., Periaux, J., and Wheeler, M.F. (eds.) Computational Science for the 21st Century, Wiley, Chichester, 1997, 113–118.

    Google Scholar 

  89. R. Glowinski and C.H. Li, On the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of the wave equation, C.R. Acad. Sc., Paris, t. 311 (1990), Série I, 135–142.

    MathSciNet  Google Scholar 

  90. Glowinski, R., C.H. Li, and J.L. Lions, A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods, Japan J. Applied Math., 7 (1990), 1–76.

    MathSciNet  Google Scholar 

  91. R. Glowinski and J.L. Lions, Exact and approximate controllability for distributed parameter systems, Part II, Acta Numerica 1995, Cambridge University Press, 1995, 159–333.

    Google Scholar 

  92. M. Crouzeix and P.A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations, Revue Française d’Automatique, Informatique et Recherche Opérationnelle, R3 (1973), 33–76.

    MathSciNet  Google Scholar 

  93. J.E. Roberts and J.M. Thomas, Mixed and hybrid methods. In Ciarlet, P.G., and Lions, J.L. (eds.) Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam, 1991, 523–639.

    Google Scholar 

  94. R. Verfurth, Error estimates for a mixed finite element approximation of the Stokes problem, Revue Française d’Automatique, Informatique et Recherche Opérationelle, Anal. Numer., 18 (1984), 175–182.

    MathSciNet  Google Scholar 

  95. R. Glowinski, T.W. Pan, T.I. Hesla, and D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flow, Int. J. Multiphase Flow, 25 (1999), 755–794.

    Article  Google Scholar 

  96. R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, and J. Periaux, A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: Application to particulate flow, Int. J. Numer. Meth. in Fluids, 30 (1999), 1043–1066.

    Google Scholar 

  97. R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, and J. Periaux, A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: Application to particulate flow, Comp. Meth. Appl. Mech. Eng., 184 (2000), 241–267.

    Article  MathSciNet  Google Scholar 

  98. R. Glowinski, T.W. Pan, T.I. Hesla, D.D. Joseph, and J. Periaux, A fictitious domain approach to the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies: Application to particulate flow, J. Comp. Phys., 169 (2001), 363–426.

    MathSciNet  Google Scholar 

  99. S. Turek, A comparative study of time-stepping techniques for the incompressible Navier-Stokes equations: from fully implicit non-linear schemes to semi-implicit projection methods, Int. J. Num. Math. in Fluids, 22 (1996), 987–1011.

    MathSciNet  MATH  Google Scholar 

  100. E.J. Dean, R. Glowinski, A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow, G.R. Acad. Sci. Paris, t. 325, Série I, (1997), 783–791.

    MathSciNet  Google Scholar 

  101. E. Dean, R. Glowinski, T.-W. Pan, A wave equation approach to the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations, in Mathematical and numerical aspects of wave propagation, J. De Santo ed., SIAM, Philadelphia, 1998, 65–74.

    Google Scholar 

  102. R. Glowinski, L.H. Juarez, Finite element method and operator splitting for a time-dependent viscous incompressble free surface flow, Computational Fluid Dynamics Journal, 9 (2003), 459–468.

    Google Scholar 

  103. R. Glowinski, O. Pironneau, Finite Element Methods for Navier-Stokes Equations, Annu. Rev. Fluid Mech., 24 (1992), 167–204.

    Article  MathSciNet  Google Scholar 

  104. C. Johnson, Streamline diffusion methods for problems in fluid mechanics, in Finite Element in Fluids 6, R. Gallagher ed., Wiley, 1986.

    Google Scholar 

  105. U. Ghia, K.N. Ghia, and C.T. Shin, High-Reynolds solutions for incompressible flow using Navier-Stokes equations and a multigrid method, J. Comp. Phys., 48 (1982), 387–411.

    Google Scholar 

  106. R. Schreiber, H.B. Keller, Driven cavity flow by efficient numerical techniques, J. Comp. Phys., 40 (1983), 310–333.

    MathSciNet  Google Scholar 

  107. C.H. Bruneau and C. Jouron, Un nouveau schéma décentré pour le problème de la cavité entraînée, C.R. Acad. Sci. Paris, t. 307, Série I (1988), 359–362.

    MathSciNet  Google Scholar 

  108. J. Shen, Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comp. Phys., 95 (1991), 228–245.

    MATH  Google Scholar 

  109. O. Goyon, High-Reynolds number solutions of Navier-Stokes equations using incremental unknowns, Comput. Methods Appl. Mech. Engrg., 130 (1996), 319–335.

    Article  MATH  Google Scholar 

  110. F. Auteri, N. Parolini, L. Quartapelle, Numerical investigation on the stability of singular driven cavity flow, J. Comp. Phys., 183 (2002), 1–25.

    MathSciNet  Google Scholar 

  111. S. Fujima, M. Tabata, Y. Fukasawa, Extension to three-dimensional problems of the upwind finite element scheme based on the choice up-and down wind points, Comp. Meth. Appl. Mech. Eng., 112 (1994), 109–131.

    MathSciNet  Google Scholar 

  112. H.C. Ku, R.S. Hirsh, T.D. Taylor, A pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations, J. Comp. Phys., 70 (1987), 439–462.

    Google Scholar 

  113. T.P. Chiang, W.H. Sheu, R.R. Hwang, Effect of Reynolds number on the eddy structure in a lid-driven cavity, Int. J. Numer. Meth. in Fluids, 26 (1998), 557–579.

    Google Scholar 

  114. A.K. Prasad and J.R. Koseff, Renolds number and end-wall efftects on a lid-driven cavity flow, Phys. Fluids, A 1 (1989), 208–218.

    Google Scholar 

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Dedicated to Jacques-Louis Lions (1928-2001)

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Glowinski, R., Pan, TW., Lorenzo Hector Juarez, V., Dean, E. (2005). Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction. In: Capasso, V., Périaux, J. (eds) Multidisciplinary Methods for Analysis Optimization and Control of Complex Systems. Mathematics in Industry, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27167-8_2

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