The diffusive strip method for scalar mixing in two dimensions
The diffusive strip method for scalar mixing in two dimensions
复制标题
二维标量混合的扩散带法
DOI：
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发表时间：
2010
影响因子：
3.7
通讯作者：
E. Villermaux
中科院分区：
文献类型：
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作者：
P. Meunier;E. Villermaux
本文介绍了二维平流场中标量混合的一种新的数值研究方法。采用运动学方法计算了材料平流带的位置，并假设扩散带的厚度小于其局部曲率半径，利用计算得到的沿带材的局部拉伸率求解了对流扩散问题。这种普遍合理的假设将数值问题简化为沿条计算单个变量，从而使该方法非常快速，并适用于任何大的psamclet数。然后，该方法用于记录混沌正弦流的混合特性，为此，我们将全局量（光谱，浓度概率分布函数（pdf），增量）与流缠绕的条带的分布拉伸联系起来，可能与自身重叠。数值结果表明，带材伸长率的PDF服从对数正态分布，是随机乘法过程的特征。这一性质导致了对场的光谱和孤立带的标量浓度的PDF的精确分析预测。本文的模拟提供了一种独特的方法来发现由重叠条带随机叠加而成的复杂混合物的相互作用规则，从而通过自卷积获得稳定的浓度pdf。
We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.