自适应时间步长法在非饱和渗流中的应用研究

Application of adaptive time step method to unsaturated seepage flow

Richards方程是非饱和渗流理论的基本方程,常用数值方法结合有效的迭代技术进行求解,时间步长调整方法常用来提高计算效率。为探究不同自适应时间步长法的数值表现,采用有限单元法结合自适应松弛Picard法和自适应时间步长法,开发了非饱和渗流有限元程序。通过模拟非饱和渗流算例,研究了不同自适应时间步长法对计算精度与效率的影响。结果表明,开发的程序是实用和可靠的,在时间步长发生较大变化时也能保证计算的稳定性。直接推断法虽然简单高效,但在求解迭代收敛难度较大的问题时,该方法难以保证良好的计算精度。截断误差法的数值表现受截断误差阈值影响,具有阈值越小,精度越高、效率越低;阈值越大,精度越低、效率越高的特点,通过调整阈值,该方法能更好地平衡计算精度和效率。研究成果对于高效非饱和渗流有限元程序的开发和应用具有一定的参考价值。

Richards equation is the fundamental equation in unsaturated seepage theory.It is commonly solved using numerical methods combined with effective iterative techniques.Time step adjustment methods are frequently used to enhance computational efficiency.To investigate the numerical performance of different adaptive time step methods,a finite element procedure employing the FEM combined with the adaptive relaxed Picard method and adaptive time step methods was developed.The effects of different adaptive time step methods on the computational accuracy and efficiency were assessed through simulations of unsaturated seepage problems.The results demonstrate that the developed procedure is practical and reliable,and it can guarantee the stability even when the time step changes significantly;the heuristic method is simple and efficient but may struggle to ensure high computational accuracy in problems with challenging iterative convergence;the numerical performance of the truncation error method is influenced by the truncation error threshold,with a smaller threshold leading to higher accuracy but lower efficiency,while a larger threshold resulting in lower accuracy but higher efficiency,and by adjusting the threshold,the truncation error method can achieve a better balance between computational accuracy and efficiency.The research findings are valuable for advancing and applying efficient unsaturated seepage finite element programs.