閉鎖性水域における汚染源特定のためのリバースシミュレーション

Abstract

Reverse simulation was proposed to specify the source of pollutant in closed water. One of the major problems of reverse simulation is the numerical instability of computation. This instability is caused by the high-frequency rounding errors. A Gaussian filter was used for the spatial distribution of pollutant or of the flux of pollutant to eliminate the instability. The effects of filtering operation were verified by comparing the results of forward and reverse simulations. Forward simulation was executed assuming that pollutant flows out from the west coast of Lake Biwa as an example of closed water. The final result of forward simulation was used as the initial condition of reverse simulation. The concentration of pollutant was solved inversely using the current velocity obtained in forward simulation. As a result, the instability of reverse simulation was suppressed by applying the Gaussian filter for the spatial distribution of pollutant, while the concentration of pollutant was more diffusive than that of forward simulation. When the Gaussian filter was applied to the special distribution of the flux of pollutant, the accuracy of reverse simulation was improved. This is because the high-frequency rounding errors were mainly suppressed by the fourth-order derivative term. The filter width is a key parameter to determine the accuracy of reverse simulation. It was relatively larger in the present study than that in the existing studies for simpler flows. This may be attributed to the numerical instability caused by complex topography and boundary condition. In addition, the distribution of the concentration of pollutant in reverse simulation was more circular than that in the forward simulation since the filtering operation was more effective where the spatial gradient of pollutant was larger. The filter width should be determined reasonably with examining the sources of the numerical instability as future studies.