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

[1]  Roland Glowinski,et al.  Splitting Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations. , 1984 .

[2]  Mordecai Avriel,et al.  Nonlinear programming , 1976 .

[3]  R. Glowinski,et al.  FINITE ELEMENT METHODS FOR NAVIER-STOKES EQUATIONS , 1992 .

[4]  R. Temam Navier-Stokes Equations , 1977 .

[5]  E. Zeidler Nonlinear functional analysis and its applications , 1988 .

[6]  Jean E. Roberts,et al.  Mixed and hybrid methods , 1991 .

[7]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[8]  G. Golub,et al.  Iterative solution of linear systems , 1991, Acta Numerica.

[9]  R. Glowinski,et al.  Exact and approximate controllability for distributed parameter systems , 1995, Acta Numerica.

[10]  Roland Glowinski,et al.  A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow , 1997 .

[11]  A. Chorin Numerical solution of the Navier-Stokes equations , 1968 .

[12]  A. D. Young,et al.  An Introduction to Fluid Mechanics , 1968 .

[13]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[14]  Michel Crouzeix,et al.  Exercices d'analyse numérique des équations différentielles , 1993 .

[15]  Jean Leray Aspects de la mécanique théorique des fluides , 1994 .

[16]  J. M. Thomas,et al.  Introduction à l'analyse numérique des équations aux dérivées partielles , 1983 .

[17]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[18]  O. Pironneau,et al.  Error estimates for finite element method solution of the Stokes problem in the primitive variables , 1979 .

[19]  F. Rühs,et al.  J. L. Lions, Équations Différentielles Opérationnelles et Problèmes aux Limites. IX + 292 S. Berlin/Göttingen/Heidelberg 1961. Springer-Verlag. Preis geb. 64,— , 1962 .

[20]  E. Fernández-Cara,et al.  The convergence of two numerical schemes for the Navier-Stokes equations , 1989 .

[21]  J. Lions Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[22]  Roland Glowinski,et al.  Computational science for the 21st Century , 1997 .

[23]  Alexandre J. Chorin,et al.  On the Convergence of Discrete Approximations to the Navier-Stokes Equations , 1969 .

[24]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[25]  Jean Leray,et al.  Sur le mouvement d'un liquide visqueux emplissant l'espace , 1934 .

[26]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[27]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[28]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .

[29]  P. Raviart Finite element methods and Navier-Stokes equations , 1979 .

[30]  R. Schnabel,et al.  A view of unconstrained optimization , 1989 .

[31]  A. Majda,et al.  Rates of convergence for viscous splitting of the Navier-Stokes equations , 1981 .

[32]  A. Chorin A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[33]  R. Hwang,et al.  Effect of Reynolds number on the eddy structure in a lid-driven cavity , 1998 .

[34]  C. Kelley Iterative Methods for Linear and Nonlinear Equations , 1987 .

[35]  J. Daniel On the approximate minimization of functionals , 1969 .

[36]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[37]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[38]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[39]  G. Marchuk Splitting and alternating direction methods , 1990 .

[40]  R. Glowinski,et al.  A distributed Lagrange multiplier/fictitious domain method for particulate flows , 1999 .

[41]  J. Lions Equations Differentielles Operationnelles , 1961 .

[42]  G. Marchuk Methods of Numerical Mathematics , 1982 .

[43]  R. Glowinski,et al.  Numerical methods for the navier-stokes equations. Applications to the simulation of compressible and incompressible viscous flows , 1987 .

[44]  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 , 1996 .

[45]  R. Glowinski,et al.  Incompressible Computational Fluid Dynamics: On Some Finite Element Methods for the Numerical Simulation of Incompressible Viscous Flow , 1993 .

[46]  J. Desanto Mathematical and numerical aspects of wave propagation , 1998 .

[47]  R. Temam Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II) , 1969 .

[48]  Jacques Periaux,et al.  A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow , 2000 .

[49]  François Thomasset,et al.  Implementation of Finite Element Methods for Navier-Stokes Equations , 1981 .

[50]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[51]  W. Prager,et al.  Introduction of Mechanics of Continua , 1962 .

[52]  Nicola Parolini,et al.  Numerical investigation on the stability of singular driven cavity flow , 2002 .

[53]  R. Glowinski,et al.  A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods , 1990 .

[54]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[55]  Jim Douglas,et al.  An absolutely stabilized finite element method for the stokes problem , 1989 .

[56]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[57]  R. Glowinski,et al.  Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics , 1987 .

[58]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[59]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[60]  Jacques Periaux,et al.  A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies : Application to particulate flow , 1999 .

[61]  R. Glowinski,et al.  On the numerical implementation of eht Hilbert uniqueness method for the exact boundary controllability of the wave equation , 1990 .

[62]  R. Sani,et al.  Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow , 1998 .

[63]  P. G. Ciarlet,et al.  Basic error estimates for elliptic problems , 1991 .

[64]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[65]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[66]  M. J. D. Powell,et al.  Restart procedures for the conjugate gradient method , 1977, Math. Program..

[67]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[68]  E. Boschi Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .

[69]  Randall J. LeVeque,et al.  Numerical methods based on additive splittings for hyperbolic partial differential equations , 1981 .

[70]  R. Glowinski,et al.  Supercomputer solutions of partial differential equation problems in computational fluid dynamics and in control , 1989 .

[71]  Marcel Lesieur,et al.  Turbulence in fluids , 1990 .

[72]  J. Cahouet,et al.  Some fast 3D finite element solvers for the generalized Stokes problem , 1988 .

[73]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[74]  J. Koseff,et al.  Reynolds number and end‐wall effects on a lid‐driven cavity flow , 1989 .

[75]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[76]  R. Glowinski Finite element methods for incompressible viscous flow , 2003 .

[77]  Olivier Goyon,et al.  High-Reynolds number solutions of Navier-Stokes equations using incremental unknowns , 1996 .

[78]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .

[79]  P. Kloucek,et al.  Stability of the fractional step T-scheme for the nonstationary Navier-Stokes equations , 1994 .

[80]  E. Hopf,et al.  Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet , 1950 .

[81]  R. Glowinski,et al.  Viscous Flow Simulation by Finite Element Methods and Related Numerical Techniques , 1985 .

[82]  A General Convergence Result for Unconstrained Minimization Methods , 1972 .

[83]  L. Quartapelle,et al.  Numerical solution of the incompressible Navier-Stokes equations , 1993, International series of numerical mathematics.

[84]  H. Kreiss,et al.  Initial-Boundary Value Problems and the Navier-Stokes Equations , 2004 .

[85]  T. Taylor,et al.  A Pseudospectral method for solution of the three-dimensional incompressible Navier-Stokes equations , 1987 .

[86]  Jean Leray,et al.  Essai sur les mouvements plans d'un fluide visqueux que limitent des parois. , 1934 .

[87]  Fujima Shoichi,et al.  Extension to three-dimensional problems of the upwind finite element scheme based on the choice of up- and downwind points , 1994 .

[88]  M. J. D. Powell,et al.  Some convergence properties of the conjugate gradient method , 1976, Math. Program..

[89]  Jorge Nocedal,et al.  Theory of algorithms for unconstrained optimization , 1992, Acta Numerica.

[90]  Rolf Rannacher,et al.  Numerical methods for the Navier-Stokes equations , 1994 .

[91]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[92]  R. Glowinski,et al.  Numerical Methods for Nonlinear Variational Problems , 1985 .

[93]  O. Pironneau Finite Element Methods for Fluids , 1990 .

[94]  Jie Shen,et al.  Hopf bifurcation of the unsteady regularized driven cavity flow , 1991 .

[95]  Roger Temam,et al.  On the theory and numerical analysis of the Navier-Stokes equations , 1973 .

[96]  J. Lions,et al.  Équations Différentielles Opérationnelles Et Problèmes Aux Limites , 1961 .

[97]  Earll M. Murman,et al.  Progress and Supercomputing in Computational Fluid Dynamics , 1985 .

[98]  Michel Fortin Finite element solution of the Navier—Stokes equations , 1993, Acta Numerica.

[99]  Gene H. Golub,et al.  Some History of the Conjugate Gradient and Lanczos Algorithms: 1948-1976 , 1989, SIAM Rev..

[100]  Luc Tartar,et al.  Topics in nonlinear analysis , 1978 .

[101]  H. B. Keller,et al.  Driven cavity flows by efficient numerical techniques , 1983 .

[102]  Alexandre M. Bayen,et al.  Computational Techniques for the Verification and Control of Hybrid Systems , 2005 .