By taking example of the 2D Navier-Stokes equations, a kind of improved version of the nonlinear Galerkin method of Marion-Temam type based on the new concept of the inertial manifold with delay (IMD) is presented, which is focused on overcoming the defect that the feasibility of the M-T type nonlinear Galerkin method heavily depended on the least solving scale. It is shown that the improved version can greatly reduce the feasible conditions as well as preserve the superiority of the former version. Therefore, the version obtained here is an applicable, high performance and stable algorithm.
nonlinear Galerkin method inertial manifold with delay Navier-Stokes equation
Chinese Library Classification
2000 MR Subject Classification
65M12 65M70 76D05
This is a preview of subscription content, log in to check access.
SHEN Jie, Temam R. Nonlinear Galerkin method using Chebyshev and Legendre polynomials I: the one-dimensional case[J].SIAM J Numer Anal, 1995,32(1):215–234.MathSciNetCrossRefzbMATHGoogle Scholar
LI Kai-tai, HOU Yan-ren. Fourier nonlinear Galerkin method for the Navier-Stokes equations[J].Discrete and Continuous Dynamical Systems, 1996,2(4):497–524.MathSciNetCrossRefGoogle Scholar
Dubois T, Jauberteau F, Marion M,et al. Subgrid modelling and the interaction of small and large wavelengths in turbulent flows[J].Computer Physics Communications, 1991,65(1–3):100–106.zbMATHMathSciNetCrossRefGoogle Scholar