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Journal of Applied Mathematics
Volume 2012, Article ID 847864, 16 pages
Research Article

Study on the Dependence of Reverse Simulation for Identifying a Pollutant Source on Grid Resolution and Filter Width in Cavity Flow

1Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
2Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan

Received 16 December 2011; Revised 2 March 2012; Accepted 3 March 2012

Academic Editor: Fu-Yun Zhao

Copyright © 2012 Satoshi Abe et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


When a hazardous substance is diffused, it is necessary to identify the pollutant source and respond immediately. However, there are many cases in which damage is caused without a clear understanding of where the pollutant source is located. There are three groups of identifying pollutant source information (Liu and Zhai, 2007): the probability method, forward method, and backward method. In our previous study, we proposed reverse simulation, which is categorized as a backward method (Abe and Kato, 2011). Numerical instability by negative diffusion is a principal problem in the backward method. In order to improve the problem, we applied a low-pass filter operation to the concentration flux in the RANS analysis. The simulation secured the numerical stability. However, reverse simulation accuracy is expected to depend on the grid resolution and filter width. In this paper, we introduce reverse simulation results in cavity flow. In particular, we survey the dependence of reverse simulation accuracy on the grid resolution and filter width. Moreover, we discuss the dependence of reverse simulation on the grid resolution and filter width with a one-dimensional diffusion equation. As a result, we found that the simulated negative diffusion varies greatly among the grid resolution and filter width.