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There are a very rich variety of nonlinear phenomena in aerodynamics.In particular,the motion of aerodynamics is often accompanied by the formation of transitional zones,where parameters(velocity,density,pressure,temperature,etc.)vary rapidly.Three types of transitional phenomena,namely,flow separation,stall and shock wave,are analyzed and presented from viewpoint of nonlinear dynamics.The phenomena listed above,which are of prime importance in air intakes,drag,lift etc.,are encountered frequently in the flow around aircraft with supersonic speed.One of the common behaviors of the phenomena is the sharp jumping or discontinuities as the Reynolds becomes higher or the viscosity coefficient is lower.The results show that stall and shock wave are the result from saddle-node bifurcation,and flow separation point is a semi-saddle.More,the study shows the flow separation,stall and shock wave can be controlled feasibly by the periodical perturbation or excitation.As a conclusion,all results can provide a fundamental understanding of the nonlinear phenomena relevant to shock wave and other complicated nonlinear phenomena.Model reduction is very important in the numerical analysis or simulation for continuum mechanics.The Inertial manifold,which is compact set,is introduced to the dissipative nonlinear evolution dynamic system.Multilevel Finite Element Method is used to approach the Approximate Inertial Manifolds(AIMs)from viewpoint of nonlinear dynamics,in the computational fluid dynamics.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 obtained.Transient phenomena in flow,such as the generation and evolution of flow separation and vortex shedding,are studied from Lagrangian viewpoint.The two typical flows,evolution of the symmetric separation bubbles and periodic vortex shedding,and the transition process between them,are analyzed in terms of Lagrangian coherent structures(LCSs).Results show that the drag is closely related with the evolution of flow separation and vortex shedding.The transports in these transient processes show that the enhancement of transport between main flow and separated area can suppress the flow separation,inducing the formation of vortices and the drop of the pressure in the separated area.