| 李茹,鲁海峰.潜水一维非稳定流方程的数值求解与工程应用[J].唐山学院学报,2022,35(6):1-7 |
| 潜水一维非稳定流方程的数值求解与工程应用 |
| Numerical Solution and Engineering Application of Phreatic One-Dimensional Unsteady Flow Equation |
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| DOI：10.16160/j.cnki.tsxyxb.2022.06.001 |
| 中文关键词: 潜水 偏微分方程 一维非稳定流方程 有限差分法 分离变量法 |
| 英文关键词: phreatic partial differential equation one-dimensional unsteady flow equation finite difference method variable separation method |
| 基金项目:国家自然科学基金项目(41977253);安徽省高等学校自然科学研究重大项目(KJ2019ZD11) |
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| 中文摘要: |
| 针对潜水一维非稳定流方程,先分别采用分离变量法和有限差分法进行求解,然后对比解析解结果,讨论显式差分法和隐式差分法的求解精度,最后将研究成果应用在某基坑降水水位预测中。研究结果表明:采用分离变量法可有效求解一类边界下潜水一维非稳定流方程;在相同密度网格剖分下,显式差分法较隐式差分法的求解精度要高,但显式差分法对网格剖分要求较高,实际应用时可根据计算精度以及计算效率等要求综合选用求解方法。 |
| 英文摘要: |
| Aiming at the phreatic one-dimensional unsteady flow equation, the separation variable method and the finite difference method are respectively used to solve it. Then based on the comparison of the analytical solution, the solution accuracy of the explicit and the implicit difference methods are discussed. Finally,the research results are applied to predict the dewatering water level of a foundation pit. The results show that the separation variable method can effectively solve the phreatic one-dimensional unsteady flow equation under a certain boundary. The numerical solution shows that under the same grid subdivision, the solution accuracy of the explicit difference method is higher than that of the implicit difference method. However, The former method requires higher grid subdivision. Therefore, the solution method should be selected according to the requirements of calculation accuracy and efficiency in practical application. |
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