Stream–aquifer interaction process plays an important role in modulating flood wave propagation in a channel. The most elementary understanding of stream–aquifer interaction can be interpreted by the flux direction between a surface water body and the underlying aquifer. At the time of floods, stream stage rises, and the water gets infiltrated into the aquifer, and this process gets reversed at the time when the stream stage gets declined. Therefore, an integrated mechanism between the surface and subsurface flows is particularly important for models, where the response of the system is based on simultaneous interactions between these two major flow domains. In this study, numerical simulation of a flood wave has been demonstrated considering stream–aquifer interaction. The calibration has been executed on a hypothetical flood event accessed by routing a known stage hydrograph for a channel reach having a rectangular cross section which fully penetrates the adjoining aquifer given by Zitta and Wiggert (Water Resour Res 7:1341–1345, 1971). A simplified mathematical approach, based on Darcy’s law, has been presented here for the solution of groundwater flow equations. The results obtained from the adopted procedure are also compared with the solution proposed by Zitta and Wiggert in 1971. The NSE and RMSE (m³/s) estimate assessed for the simulated hydrographs using the proposed methodology with respect to the procedure adopted by Zitta and Wiggert (Water Resour Res 7:1341–1345, 1971) is 0.9983 and 0.8544, respectively. Therefore, the use of Simpson’s (3/8)-rule is not suggestible due to its complicated calculation and its sensitivity, and it is better to use the proposed simplified approach for the evaluation of lateral flow.

流—水层相互作用过程在调制洪水波在河道中的传播中起着重要作用。可以通过地表水体与下层含水层之间的通量方向来解释对水-含水层相互作用的最基本的理解。在洪水发生时，水位上升，水渗透到含水层中，当水位下降时，这一过程被逆转。因此，对于模型而言，地表和地下流动之间的整合机制尤为重要，因为系统的响应基于这两个主要流动域之间的同时相互作用。在这项研究中，考虑了水-水层相互作用，证明了洪水波的数值模拟。校准是在假设洪水事件中执行的，该洪水事件通过路由已知阶段的水文图来获取具有矩形横截面的河段，该河段完全穿透了Zitta和Wiggert给出的相邻含水层（Water Resour Res 7：1341-1345，1971）。本文提出了一种基于达西定律的简化数学方法，用于求解地下水流方程。从采用的程序获得的结果也与Zitta和Wiggert在1971年提出的解决方案进行了比较。NSE和RMSE（m 这里已经提出了地下水流方程的解决方案。从采用的程序获得的结果也与Zitta和Wiggert在1971年提出的解决方案进行了比较。NSE和RMSE（m 这里已经提出了地下水流方程的解决方案。从采用的程序获得的结果也与Zitta和Wiggert在1971年提出的解决方案进行了比较。NSE和RMSE（m³ / s），使用拟议的方法对Zitta和Wiggert（Water Resour Res 7：1341-1345，1971）采用的拟议方法对模拟水文图进行评估的估计分别为0.9983和0.8544。因此，由于辛普森（3/8）规则计算复杂且灵敏度高，因此不建议使用，并且最好使用所提出的简化方法来评估侧向流动。