通用函数边界下潜水非稳定流模型的解及应用

Solution and Application of Submersible Unsteady Flow Model under Universal Function Boundary

针对半无限域河渠附近潜水非稳定运动经典模型中河渠水位边界条件概化的局限性,本文在经典模型的基础之上将河渠水位变化过程概化为通用函数形式,并采用Laplace变换方法对模型进行处理,结合Laplace变换中的微分定理和卷积定理,给出模型的解析解;同时,为探讨解在实际问题中的运用,本文对河渠水位变化过程进行Lagrange线性插值,并结合相关实测水位数据利用Matlab软件对含水层参数进行求解;结果表明,通用函数形式河渠水位边界条件下给出的模型解析式形式较为简洁,解的构成也均为常规函数,结合插值函数,经处理后进行含水层参数求解,方法简便且结果精度较高,具有较好的推广价值。

In view of the limitations of the generalization of the water level boundary conditions in the canal unsteady motion model near the semi-infinite domain canal,this paper will generalize water level change process of the canal as a general function form based on the classic model,use the Laplace transform method to process the model and give the analytical solution of the model with the differential theorem and convolution theorem in Laplace transform.To explore the application of the solution in practical problems,this paper analyzes the water level change process of the canal by Lagrange interpolation,and uses Matlab software to solve the aquifer parameters with the relevant measured water level data.The results show that the analytic form is relatively simple,and the composition of the solution is also a regular function.Combined with the interpolation function,the aquifer parameters are solved after processing.The method is simple and the result precision is high,which has good popularization value.