Numerical algorithm for solving the problem of a nonlinear three-dimensional mathematical model for predicting changes in groundwater levels
Article Sidebar
Main Article Content
Abstract
The article considers the problem of forecasting changes in groundwater levels using numerical methods based on a three-dimensional nonlinear mathematical model. The model takes into account factors affecting the dynamics of the aquifer - water intake wells, evaporation and other external sources. The model, based on differential equations, describes the movement of groundwater, and an algorithm for solving it using the alternating direction method is proposed. When performing numerical calculations, the model is initially expressed through dimensionless quantities, which is one of the ways to improve the convenience of obtaining calculation results. The calculation results allow us to estimate and predict changes in water levels under various conditions. This approach can be used for effective water resource management and the development of environmental monitoring systems.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Huang, C.‐S., Wang, Z., Lin, Y.‐C., Yeh,H.‐D., & Yang, T. (2020). New analytical models for flow induced by pumping in a stream‐aquifer system: A new Robin boundary condition reflecting joint effect of streambed width and storage. Water Resources Research, 56, e2019WR026352. https://doi.org/10.1029/2019WR026352.
Абуталиев Ф.Б. Решение задач неустановившейся фильтрации. -Ташкент: фан, 1972.-207 с.
Lin LIN, Jin-Zhong YANG, Bin ZHANG, Yan ZHU, A simplified numerical model of 3-D groundwater and solute transport at large scale area, Journal of Hydrodynamics, Ser. B, Volume 22, Issue 3, 2010, Pages 319-328, ISSN 1001-6058, https://doi.org/10.1016/S1001-6058(09)60061-5.
Xu-Sheng Wang, Hongbin Zhan, A new solution of transient confined–unconfined flow driven by a pumping well, Advances in Water Resources, Volume 32, Issue 8, 2009, Pages 1213-1222, https://doi.org/10.1016/j.advwatres.2009.04.004.
Hantush, M. S. (1967). Depletion of flow in right-angle stream bends by steady wells. Water Re-sources Research, 3(1), 235–240. doi:10.1029/wr003i001p00235.
Xiong, M., Tong, C., & Huang, C.-S. (2021). A new approach to three-dimensional flow in a pumped confined aquifer connected to a shallow stream: Near-stream and far-from-stream groundwater ex-tractions. Water Resources Research, 57, e2020WR028780. https://doi.org/10.1029/2020WR028780.
Daliev Sh., Sirojiddinov F., Khaitov O., Developing Mathematical Models to Study Changes in Groundwater Levels and Salt Concentration E3S Web Conf. 589 03011 (2024) DOI: 10.1051/e3sconf/202458903011.
Ravshanov N., Daliev S., Abdullaev Z., Khafizov O. Ground and confined underground waters and their salt content // IEEE International Conference on Information Science and Communications Technologies. – 2020. – P. 1-12.
Ravshanov N., Daliev S. Non-linear mathematical model to predict the changes in underground wa-ter level and salt concentration // Journal of Physics: Conference Series. – 2020. – Vol. 1441. – Art. 012163.
Ravshanov N., Zagrebina S.A., Daliev Sh.K. Numerical simulation of unsteady underground water filtration in a porous medium // Problems of computational and applied mathematics. – 2019. – No. 4. – P. 12-30.
Khabibullaev I., Murodullaev B.T., Haqnazarova D.O. Numerical modeling of groundwater filtra-tion processes in irrigation areas // Problems of computational and applied mathematics. – 2023. – No. 3(49). – P. 21-32.
Khabibullaev I., Murodullaev B.T., Haqnazarova D.O. 2023. Three-demensional mathematical model of groundwater level changes in irrigated land // Problems of computational and applied mathematics. – 2023. – No. 5. – P. 44-55.
Guo W., Langevin C.D. User’s guide to SEAWAT: a computer program for simulation of three-dimensional variable-density ground-water flow // US Geological Survey. – 2002. –Vol. 1, No. 434.
Hornberger G.M., Boyer E.W. Recent advances in watershed modelling // Reviews of Geophysics. – 1995. – No. 33(S2). – P. 949-957.
Dassargues A. Hydrogeology: groundwater science and engineering. – CRC Press, 2018.
McDonald M.G., Harbaugh A.W. A modular three-dimensional finite-difference groundwater flow model // US Geological Survey. – 1988.
Pinder G.F., Gray W.G. Finite element simulation in surface and subsurface hydrology. –Elsevier, 2013.
Reilly T.E., Harbaugh A.W. Guidelines for evaluating ground-water flow models. – DIANE Publish-ing, 2004.
Simunek J. et al. HYDRUS-1D. Simulating the one-dimensional movement of water, heat, and mul-tiple solutes in variably-saturated media, version, 2. – 1998.
Anderson M.P., Woessner W.W., Hunt R.J. Applied groundwater modeling: simulation of flow and advective transport. – Academic press, 2015.
Самарский А.А., Итерационные методы для сеточных уравнений. Математические структуры. Вычислительная математика. Математическое моделирование. Труды, посвященные 60-летию ак. Илиева, София, 1975, с.153-164.
Яненко Н.Н., Метод дробных шагов решения многомерных задач математической физики. издательство «Наука»- Сибирское отделение Новосибирск-1967 г. стр. 197.