Title of article :
Model reduction on inertial manifolds for N–S equations approached by multilevel finite element method
Author/Authors :
Zhang، نويسنده , , Jiazhong and Ren، نويسنده , , Sheng and Mei، نويسنده , , Guanhua، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
11
From page :
195
To page :
205
Abstract :
Approximate Inertial Manifolds (AIMs) is approached by multilevel finite element method, which can be referred to as a Post-processed nonlinear Galerkin finite element method, and is applied to the model reduction for fluid dynamics, a typical kind of nonlinear continuous dynamic system from viewpoint of nonlinear dynamics. By this method, each unknown variable, namely, velocity and pressure, is divided into two components, that is the large eddy and small eddy components. 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 by AIMs, and consequently a coarse grid finite element space and a fine grid incremental finite element space are introduced to approach the two components. As an example, the flow field of incompressible flows around airfoil is simulated numerically and discussed, and velocity and pressure distributions of the flow field are obtained accurately. The results show that there exists less essential degrees-of-freedom which can dominate the dynamic behaviors of the discretized system in comparison with the traditional methods, and large computing time can be saved by this efficient method. In a sense, the small eddy component can be captured by AIMs with fewer grids, and an accurate result can also be obtained.
Keywords :
approximate inertial manifolds , Multilevel finite element method , Nonlinear dynamics , fluid dynamics , Model reduction
Journal title :
Communications in Nonlinear Science and Numerical Simulation
Serial Year :
2011
Journal title :
Communications in Nonlinear Science and Numerical Simulation
Record number :
1535608
Link To Document :
بازگشت