论文部分内容阅读
为解决Green-Ampt(GA)入渗模型只有隐格式解的问题,给出了高精度的显格式近似解,该显格式构造一组幂函数作为基函数,通过最小化近似解与精确解之间的误差,达到对GA模型的逼近。在对误差函数最小化的过程中,首先证明优化解的存在性,同时采用自适应的优化分段方法,在满足精度的条件下减少基函数的级数,达到简化计算的目的。针对入渗时间趋于无穷导致近似解发散问题,建立了修正公式,确保了该逼近方法的全局收敛性。通过与其他近似解的比较,验证了该方法的稳定性和精确性。
In order to solve the problem that the Green-Ampt (GA) infiltration model has only implicit solution, a high-precision explicit approximate solution is given. The explicit formulation constructs a set of power functions as the basis functions. By minimizing the approximate solution and the exact solution Between the error, to GA model approximation. In the process of minimizing the error function, firstly, the existence of the optimal solution is proved. At the same time, an adaptive optimal segmentation method is used to reduce the number of basis functions while satisfying the precision, so as to simplify the calculation. Aim at the problem that the infiltration time tends to infinity and the approximate solution divergence problem, a modified formula is established to ensure the global convergence of the approximation method. By comparing with other approximate solutions, the stability and accuracy of this method are verified.