倾斜地下水含水层混合3维溶质运移数值模拟

摘要

针对不规则地下水含水层中溶质运移简化数值模拟问题,根据不规则地下水含水层特点,提出了柱体单元水头梯度平均面的概念。在水头梯度平均面的基础上,采用有限单元法推导柱体单元水平向溶质通量,而柱体单元垂向溶质运移通量则采用有限差分法进行推导,通过联合利用有限单元法和有限差分法计算柱体单元节点溶质均衡项,根据不规则柱体单元溶质均衡项计算结果,编制Fortran程序,建立倾斜地下水含水层混合3维溶质运移数值模拟模型。运用该模型模拟了不同条件下地下水中溶质运移过程,将模拟结果与解析解进行对比分析,模拟得到的溶质浓度结果正确、合理。该模型适用于倾斜地下水含水层中溶质运移模拟,具有节省计算工作量,单元剖分灵活的优点。同时,当Peclet数较大时,该模型分别在水平向和垂向采用迎风加权格式进行计算,有效地消除了边界附近出现的数值跳动现象,模型也适用于Peclet数较大的情况。%The average surface of head gradient in the irregular triangular prism element was proposed to develop a simplified numerical model of solute transport in the irregular groundwater system.The results of the solute mass balance in a triangular prism element were calculated using the hybrid finite element method and the finite difference method basing on the average surface of head gradient.The net lateral solute mass in the control volume to the node was computed by the finite element method and the vertical solute mass to the node by the finite difference method.With the proposed method,the 3-D numerical model was developed and applied to simulate the solute transport in different hypothetic examples.The simulation results of the proposed model agreed well with the analytic solutions.The solute transport model,which has the advantage of saving the computational cost and can be applied to irregular aquifer system,was established on the simplified 3-D groundwater model.Furthermore,upwind finite element scheme and upwind finite difference method were used respectively in the horizontal and vertical directions,which can minimize the numerical oscillation when relatively steep concentration fronts are simulated.