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为了协调Richards方程数值模型在精度、稳定性和计算效率之间的矛盾,对时间步长进行优化控制,发展了一种变步长的计算模型。采用van Genuchten模型,将描述土壤水分运动的Richards方程(为偏微分方程)在空间上半离散后得到常微分方程组,借助于该求解器求解。针对以含水率θ为变量的Richards方程进行了试验,常微分方程组求解采用CVODE求解器,并对土壤水分特征曲线和水量平衡进行了检验。结果表明,该模型具有较高的计算精度、求解效率和稳定性。
In order to coordinate the contradiction between the accuracy, stability and computational efficiency of the Richards equation numerical model, the time step is optimized and controlled, and a computational model with variable step size is developed. Using the van Genuchten model, the Richards equation (for partial differential equations) that describes soil water movement is semi-discrete in space and is solved by means of the solver. Experiments were carried out on the Richards equation with the water content θ as a variable. The ODE solver was used to solve the ODE and the soil water characteristic curve and water balance were tested. The results show that the model has high computational accuracy, solving efficiency and stability.