Multilevel finite element method is used to approach the Approximate Inertial Manifolds (AIMs) from viewpoint of nonlinear dynamics, in the computational fluid dynamics. By this method, an unknown variable is divided into two components, namely, the large eddy and small eddy components. With the introduction of an AIMs, the interaction between large eddy and small eddy components, which is negligible if standard Galerkin algorithm is used to approach the original governing equations, is considered essentially, and consequently a coarse grid finite element space and a fine grid incremental finite element space are introduced to approach the two components. By this method, the flow field of incompressible flows around airfoil is simulated numerically as an example, and velocity and pressure distributions of the flow field are obtained accurately. The results show that there exists less degrees-of-freedom in the discretized system in comparison with the traditional methods, and large computing time can be saved by this efficient method. The small eddy component can be captured by AIMs, and an accurate result can also be obtained.
Model Reduction Global Attractor Quadrangle Element Finite Element Space Inertial Manifold
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This research is supported by Program for New Century Excellent Talents in University in China, No. NCET-07-0685.
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