The nonlinear Galerkin method in computational fluid dynamics

We discuss here the nonlinear Galerkin method which corresponds to the projection of the equations under consideration on a nonlinear manifold close to the attractor. This method stems from the theory of inertial manifolds and approximate inertial manifolds which has proved to be a powerful tool of investigation for dynamical systems. We intend to briefly review some results concerning the attractors for the Navier-Stokes equations and their approximations

[1]  R. Temam,et al.  Modelling of the interaction of small and large eddies in two dimensional turbulent flows , 1988 .

[2]  R. Temam,et al.  On the dimension of the attractors in two-dimensional turbulence , 1988 .

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

[4]  Roger Temam,et al.  Induced trajectories and approximate inertial manifolds , 1989 .

[5]  R. Temam,et al.  Nonlinear Galerkin methods , 1989 .

[6]  Roger Temam,et al.  Inertial manifolds and multigrid methods , 1990 .

[7]  R. Temam.  Navier-Stokes Equations and Nonlinear Functional Analysis , 1987 .

[8]  R. Temam,et al.  Determining modes and fractal dimension of turbulent flows , 1985, Journal of Fluid Mechanics.

[9]  M. Bercovier.  Perturbation of mixed variational problems. Application to mixed finite element methods , 1978 .

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

[11]  M. Vishik,et al.  Attractors of partial differential evolution equations and estimates of their dimension , 1983 .

[12]  C. Foias,et al.  On the interaction of small and large eddies in two dimensional turbulent flows , 1987 .

[13]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[14]  Karl Gustafson,et al.  Cavity flow dynamics at higher reynolds number and higher aspect ratio , 1987 .

[15]  R. Temam.  Variétés inertielles approximatives pour les équations de Navier-Stokes bidimensionnelles , 1988 .

[16]  Jie Shen.  Dynamics of regularized cavity flow at high Reynolds numbers , 1989 .

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