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21.
In this paper we formulate a theorem on the persistence of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition, and give the measure estimates of parameters for the non-resonance conditions under Rüssmann’s non-degeneracy condition, which is essential for the proof of our result. 相似文献
22.
This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H1 for the velocity, as in most current numerical schemes relying on spatial discretizations of local type. 相似文献
23.
The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions. 相似文献
24.
This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
25.
Ram K. Ganesh 《国际流体数值方法杂志》1991,13(5):557-578
The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained. 相似文献
26.
Arsenic-tolerant freshwater alga Chlorella vulgaris which had been collected from an arsenicpolluted environment were tested for uptake and excretion of inorganic arsenic. Approximately half the quantity of arsenic taken up by C. vulgaris was estimated to be adhered to the extraneous coat (10 wt %) of the cell. The remainder was bioaccumulated by the cell. Both adhered and accumulated arsenic concentrations increased with an increase in arsenic(V) concentration of the aqueous phase. Arsenic(V) accumulation was affected by the growth phse: arsenic was most actively accumulated when the cell was exposed to arsenic during the early exponential phase and then accumulation decreased with an increase in culture time exposed to arsenic. The alga grew well in the modified Detmer (MD) medium containing 1 mg As(III) dm?3 and the growth curve was approximated by a ‘logistic equation’. Arsenic(III) was accumulated up to the second day of the culture time and arsenic(III) accumulation decreased with an increase in the culture time after that. Arsenic accumulation was also largely affected by various nutrients, especially by managanese, iron and phosphorus compounds. A modified MD medium with the three nutrients was proposed for the purpose of effective removal of arsenic from the aqueous phase. Using radioactive arsenate (Na2H74AsO4), the arsenic accumulated was found to be readily excreted under conditions which were unfavourable for the multiplication of C. vulgaris. 相似文献
27.
Lisa F. Shatz 《国际流体数值方法杂志》2004,44(2):147-174
The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
28.
In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd. 相似文献
29.
The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
30.
The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory. 相似文献