IMD Based Nonlinear Galerkin Method
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摘要: 针对Marion-Temam型非线性Galerkin方法可行性强烈依赖于最小解题规模的不足,利用时滞惯性流形的新思想,以二维Navier-Stokes方程为例,给出了该类非线性Galerkin方法的一种改进形式,并证明了改进后的方法在保持原方法优越性的同时,其可行性条件得到了很大的改善,从而,给出的是一种可行的高效稳定算法。
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关键词:
- 非线性Galerkin方法 /
- 时滞惯性流形 /
- Navier-Stokes方程
Abstract: 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. -
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