A Modified Algorithm of FCM for Simulating Biological and Chemical Transport Process
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摘要: 给出了有限颗粒法(FCM) 的一个修正算法, 用来模拟二维多孔介质中复杂的物理、生物化学输运现象.该算法不仅具有与早先的FCM一样的优点, 而且可以在更微观的水平上保证质量守恒, 获得更为准确的颗粒位置, 从而有利于质量交换的高精度计算.计算结果与精确解和早先的FCM的结果做了比较.Abstract: A modified algorithm of finite cell method (FCM) is presented for simulating complex physical, biological and chemical transport in porous media. It not only has the same advantages as the original finite cell method, but also can keep local mass conservation in more finer meshes, so we may get the locations of cells as well as the final results with high accuracy. Two numerical examples show the comparison between the solutions of modified FCM and original FCM and analytical solutions.
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Key words:
- groundwater pollution /
- reactive transport /
- biodegradation /
- finite cell method.
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图 1 实线所示的2个单元, 上面是移入单元, 即下游单元, 下面是移出单元, 即上游单元
Fig. 1. Two blocks shown by solid line, the upper is downstream block which maybe accept cells, the lower is the upstream block which maybe send out cells
图 2 问题1的精确解和数值解结果比较
a, b.分别是精确解在第4天、第8天的子区域平均结果; c, d.分别是修正的FCM算法在第4天、第8天模拟结果; e, f.分别是原FCM算法在第4天、第8天的模拟结果
Fig. 2. Comparison between analytical solution and FCM solutions of problem 1 on the fourth day and eighth day respectively
图 3 第4, 5, 8天的有机污染物浓度模拟结果
a, c, e.原FCM算法的计算结果; b, d, f.修正的FCM算法的模拟结果
Fig. 3. Concentrations of hydrocarbon simulated by the two FCMs on the fourth day, fifth day and eighth day respectively
表 1 数值模拟问题2时所用的各种参数值
Table 1. Values of parameters in problem 2
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