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在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法——欠松弛RFT变换方法(ATUR1)。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。
When using finite element method to solve the seepage problem of unsaturated soil, the strong nonlinearity of soil-water characteristic curve and permeability function often leads to problems such as non-convergence of iteration, large calculation error and so on. Based on the idea of variable transformation, a new method to solve unsaturated seepage problem is proposed based on the time step adaptation technique (ATUR1). The ATUR1 method greatly reduces the degree of spatial and temporal nonlinearity of the unknown in the Richards equation through variable transformation, so as to improve the computational convergence and accuracy caused by this nonlinearity. The introduction of under-relaxation technique reduces the oscillation in the iterative process and further improves the efficiency of nonlinear iterative calculation. The time step adaptation technique effectively controls the error of the whole calculation process. The numerical example shows that ATUR1 can effectively improve the computational efficiency and accuracy, which is an accurate and effective method of calculation.