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首页> 外文学位 >The application of non-linear frequency domain methods to the Euler and Navier-Stokes equations.
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The application of non-linear frequency domain methods to the Euler and Navier-Stokes equations.

机译：非线性频域方法在Euler和Navier-Stokes方程中的应用。

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This research demonstrates the accuracy and efficiency of the Non-Linear Frequency Domain (NLFD) method in applications to unsteady flow calculations. The basis of the method is a pseudo-spectral approach to recast a non-linear unsteady system of equations in the temporal domain into a stationary system in the frequency domain. The NLFD method, in principle, provides the rapid convergence of a spectral method with increasing numbers of modes, and, in this sense, it is an optimal scheme for time-periodic problems. In practice it can also be effectively used as a reduced order method in which users deliberately choose not to resolve temporal modes in the solution.; The method is easily applied to problems where the time period of the unsteadiness is known a priori. A method is proposed that iteratively calculates the time period when it is not known a priori . Convergence acceleration techniques like local time-stepping, implicit residual averaging and multigrid are used in the solution of the frequency-domain equations. A new method, spectral viscosity is also introduced. In conjunction with modifications to the established techniques this produces convergence rates equivalent to state-of-the-art steady-flow solvers.; Two main test cases have been used to evaluate the NLFD method. The first is vortex shedding in low Reynolds number flows past cylinders. Numerical results demonstrate the efficiency of the NLFD method in representing complex flow field physics with a limited number of temporal modes. The shedding frequency is unknown a priori, which serves to test the application of the proposed variable-time-period method. The second problem is an airfoil undergoing a forced pitching motion in transonic flow. Comparisons with experimental results demonstrate that a limited number of temporal modes can accurately represent a non-linear unsteady solution. Comparisons with time-accurate codes also demonstrate the efficiency gains realized by the NLFD method.
机译：这项研究证明了非线性频域（NLFD）方法在非恒定流量计算中的应用的准确性和效率。该方法的基础是伪谱方法，可以将时域中的非线性非稳态方程组重铸为频域中的平稳系统。原则上，NLFD方法提供了随着模式数量增加而频谱方法的快速收敛，并且从这个意义上讲，它是解决时间周期问题的最佳方案。实际上，它也可以有效地用作降阶方法，在这种方法中，用户故意选择不解析解决方案中的时间模式。该方法很容易应用于不稳定的时间段已知为 priorit 的问题。提出了一种方法，该方法可以迭代地计算未知的 的时间段。在频域方程的解中使用了诸如局部时间步长，隐式残差平均和多重网格之类的收敛加速技术。还介绍了一种新方法，即光谱粘度。结合对现有技术的修改，可以产生与最新的稳态流求解器相当的收敛速度。已经使用两个主要测试案例来评估NLFD方法。首先是低雷诺数流经过圆柱体时涡旋脱落。数值结果证明了NLFD方法在有限数量的时间模式下表示复杂流场物理学的效率。脱落频率是未知的 apriori ，它可以用来测试所提出的可变时间周期方法的应用。第二个问题是机翼在跨音速流中经历强制俯仰运动。与实验结果的比较表明，有限数量的时间模式可以准确地表示非线性非稳态解。与时间精确代码的比较也证明了通过NLFD方法实现的效率提高。

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