Filtering for the Inverse Problem of Convection–Diffusion Equation with a Point Source
Filtering for the Inverse Problem of Convection–Diffusion Equation with a Point Source
复制标题
点源对流扩散方程反问题的滤波
DOI：
10.1143/jpsj.81.114401
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发表时间：
2012
影响因子：
1.7
通讯作者：
S. Kato
中科院分区：
文献类型：
--
作者：
F. Hamba;S. Abe;D. Kitazawa;S. Kato
在识别污染源的反向模拟中，计算流体动力学模型的输运方程在时间上向后求解。为了抑制反模拟的数值不稳定性，采用了一些滤波方法。然而，滤波的效果还没有被清楚地解释，并且滤波器宽度的值通常通过试验和错误来确定。在这项工作中，一维和二维对流扩散方程从点源发射的物质进行了分析，检查过滤的物理意义，并推导出一种方法，用于确定过滤器的宽度提前。以正演模拟的结果为初始条件，分别采用浓度场滤波和浓度通量滤波两种滤波方法进行了反演模拟。结果表明，后者的过滤给出了更好的结果，因为四阶扩散项降低了傅里叶分量的高次模的增长率。莫洛夫...
In the reverse simulation for identifying pollutant sources the transport equations for the computational fluid dynamics model are solved backward in time. Some filtering methods are used to suppress the numerical instability of the reverse simulation. However, the effect of filtering has not been clearly explained yet and the value of filter width is often determined by trial and error. In this work the one- and two-dimensional convection–diffusion equations for matter emitted from a point source are analyzed to examine the physical meaning of filtering and to derive a method for determining the filter width in advance. Using the result of a forward simulation as the initial condition, reverse simulations are carried out with two types of filtering methods: filtering the concentration field and filtering the flux of the concentration. It is shown that the latter filtering gives better results because the fourth-order diffusion term reduces the growth rate of higher modes of the Fourier component. Moreove...