Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media
Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media
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异质介质中点状注射的传输参数和自平均特性的近似值
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发表时间：
2004
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通讯作者：
J. Eberhard
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作者：
J. Eberhard
我们专注于传输参数在非均匀介质中的流动建模的合奏周期性和高斯随机场。参数由系综平均值确定。我们研究这些平均值在多大程度上代表了单一实现中的行为。我们计算中心的质量速度和色散系数使用近似的基础上的微扰扩展的传输方程，并在朗之万方程的迭代解。与模拟相比，扰动理论再现的数值结果只有差，而迭代解产生良好的结果。使用这些近似，我们调查的自平均性能。速度的集合平均值表征了在两个集合中大时间实现的行为。在周期场系综中，色散系数不是自平均的。对于高斯系综，渐近色散系数是自平均的。然而，对于有限的时间，波动是如此之大，以至于平均值不能代表单一实现中的行为。
We focus on transport parameters in heterogeneous media with a flow modelled by an ensemble of periodic and Gaussian random fields. The parameters are determined by ensemble averages. We study to what extent these averages represent the behaviour in a single realization. We calculate the centre-of-mass velocity and the dispersion coefficient using approximations based on a perturbative expansion for the transport equation, and on the iterative solution of the Langevin equation. Compared with simulations, the perturbation theory reproduces the numerical results only poorly, whereas the iterative solution yields good results. Using these approximations, we investigate the self-averaging properties. The ensemble average of the velocity characterizes the behaviour of a realization for large times in both ensembles. The dispersion coefficient is not self-averaging in the ensemble of periodic fields. For the Gaussian ensemble the asymptotic dispersion coefficient is self-averaging. For finite times, however, the fluctuations are so large that the average does not represent the behaviour in a single realization.