非饱和带有限分析数值模拟的误差分析

由于描述包气带水分运移的Richard方程具有高度非线性,常用数值方法求解。有限分析法可以较好地保持原有问题的物理特性,近年来被广泛应用于环境及农业工程领域。基于不同的原理,目前有两种有限分析法模拟非饱和带水分运移问题,即基于局部线性化有限分析法和基于Kirchhoff变换有限分析法。为探讨两者在求解非饱和带水分运移问题时数值表现的差异性,采用已有解析解对两种方法进行初步验证;使用两个数值实验比较两种方法的计算精度;应用实测数据验证Kirchhoff变换有限分析法。相比于局部线性化有限分析法,Kirchhoff变换有限分析法能够更好地控制误差及获得更高精度的数值解。该研究对于完善非饱和带水分运移有限分析数值模拟的理论与方法有重要意义。

Analysis of errors in finite analytic numerical simulation of flow in unsaturated zone

Numerical methods are often used to solve Richards' equation due to the nonlinearity of the equation. Since Finite Analytic Method(FAM) can better keep the original physical properties of the Richards' equation, it has been widely used in the field of environmental and agricultural engineering in recent years. Based on different principles, there are two kinds of Finite Analytic Methods, namely local linearization FAM and Kirchhoff transform FAM, to simulate moisture movement in unsaturated zone. To explore the differences of numerical performances between the two kinds of FAMs, we have carried out the following researches:first, an existing analytical solution is used to preliminarily validate the two kinds of FAMs. After that, two numerical experiments are conducted to compare the accuracy of two methods. Finally, observed data are used to validate the Kirchhoff transform FAM. Compared to the local linearization FAM, Kirchhoff transform FAM can better control the calculated error and obtain higher accuracy of numerical solutions. Therefore, this study has important significance to improve the theory of FAM, which is applied to simulate unsaturated flow.