Applications of the nonlinear galerkin methods to some flow problems

摘要

A recent integrationalgorithm, the Nonlinear Galerkin Method, stemming from dynamical systems theory and developed for the long-time integration of dissipative evolution equations, is applied to the nonlinear stability problem in plane channel (Poiseuille) flow and temporally growing mixing layer. Different nonlinear Galerkin algorithms are compared with repsect to each other in terms of convergence and efficiency. The improvements with respect to classical Galerkin spectral method are shown numerically. The method seems to be promising in the context of the direct numerical simulationof the Navier-Stokes equations.