The Wind Turbine Flow Field Numerical Simulation Of Newton Method Local Convergence Analysis

Wind as a clean renewable energy has been paid more and more attention, manycountries in the world have stepped up efforts to develop wind power. If you want tomaximize the use of wind power generation, the wind machine design requires designmethod by using numerical for wind turbine design needs further optimization. In addition,the computer technique and the development of computational fluid dynamics haveprovide favorable and convenient conditions for the wind turbines to raise the level ofresearch.The wind turbine flow field is a compressible, sticky and nonstationary flow field, themathematical model of which is nonstationary, nonlinear partial differential equations ofdetermining solution. This paper was established the mathematical model in order tonumerical solution these differential equations of determining solution. And then thediscretization format was given. Finally, analysis Newton iterative format localconvergence and simulation and so on. Main contents of this thesis are described as thefollowing:(1) The wind turbine flow fields of cylinder solve area, it convenient to solve theproblem of cylindrical coordinate system rather than the right angle coordinate system.Thus, the control equations of right angle coordinate system switch to the control equationsof cylindrical coordinate system. Give out the original boundary conditions undercylindrical coordinate system, and then the corresponding determining solutions forproblems are obtained. (2) Use finite difference method directly to disperse the cylindrical coordinate systemof basic control equation. And then a nonlinear equations was given; this paper usedNewton method numerical solution for the nonlinear equations; finally given Newtoniterative format--linear equations; adopting the over relaxation method to solve this linearequations.(3) Analysis the format of the Newton iterative local convergence, given the localconvergence conditions. The key point of this paper gave the nonlinear equations ofNewton iterative format of Newton iterative convergence condition.(4) In order to validate the Newton local convergence conditions to the effectivenessand feasibility of the application of Visual Fortran computer program of the correspondingplatform.By analyzing the practical example of the results of numerical simulation analysis, itcan be seen that Newton method local convergence depends on the time step long value; todifferent time step, the convergence of the Newton method different situation; the value oftime-step length in the actual calculating can be bigger than theoretical value slightly.