空间链接器式多维通用饱和-非饱和流模型研究

多维饱和-非饱和流方程离散后生成的系数矩阵中常存在零系数，这将影响求解过程中的存储空间和计算效率。合理的系数矩阵优化方法既能保证模拟精度，又能提高模型在大规模网格单元中的计算效率及通用性。文章在多维饱和-非饱和流有限差分法基础上，预先记录不同方向上有效单元间的连接关系，避免了零系数的计算和存储，并结合矩阵标识法建立了空间链接器式多维通用饱和-非饱和流模型。通过模拟地下水位起涨、渗流面排水等四个经典案例及田间三场长历时小雨入渗过程，验证了该模型的模拟精度及计算效率。对比结果表明:该模型在多维度、不同边界条件（包括天然降雨、渗流面等）下的模拟精度与Hydrus、VSF等成熟软件相当，计算效率略低于Hydrus软件。田间模拟结果表明:VG模型中的参数n敏感性最强，需优先率定；因模型中尚未考虑大孔隙流影响，各层土壤水分响应时间滞后于实测过程；三场降雨计算时段末期，超过80%的入渗水量仍滞蓄在表层40 cm的土壤中，仅有约4%~12%的水量已转化为潜水。本文模型有望成为传统多维饱和-非饱和流模型的重要补充。

A generalized multi-dimensional saturated-unsaturated flow model based on spatial linkers

There are often some zero coefficients in the coefficient matrix after the multi-dimensional saturated-unsaturated flow equation is discretized, which will affect the storage space and calculation efficiency in the solution process. A reasonable coefficient matrix optimization method can not only guarantee the simulation accuracy, but also improve the calculation efficiency and universality of the model when it is applied in large-scale grid cells. This paper proposed a generalized multi-dimensional saturated-unsaturated flow model based on spatial linkers. Finite difference method is used to solve the multi-dimensional saturated-unsaturated flow equation. The connections between each two effective units in different directions were pre-recorded, which will avoid the calculation and storage of zero coefficients. The matrix marking method is applied to further simplify the coefficient matrix. The simulation accuracy and efficiency of the model are verified by simulating four classic cases, such as groundwater level rise and seepage surface drainage, as well as three long periods of light rain infiltration in the field. The comparison results show that the simulation accuracy of the model is comparable to some mature softwares, such as Hydrus and VSF, under multiple dimensions and different boundary conditions (including natural rainfall, seepage surface, etc.), while the efficiency is slightly lower than that with Hydrus. Field simulation results also show that the parameter n in VG model can make greatest changes in simulation results with smallest variation and needs to be calibrated in priority. Because the effect of macropore flow has not been considered in the model, the soil moisture response time of each layer lags behind the measured process. At the end of the three rainfall calculation periods, more than 80% of the infiltration water is still stored in the upper 40 cm soil layer, and only about 4%—12% of the infiltration water has been converted to phreatic water. The model in this paper is expected to be an important supplement to the traditional multi-dimensional saturated-unsaturated flow models.