Mathematical modelling of filtration processes in drainage systems with different depths of drainage

Journal of Water and Land Development

article

Volodymyr Havryliuk¹  Andrii Bomba²  Oleg Pinchuk²  Ievgenii Gerasimov²  Serhii Klimov²  Mykola Tkachuk²  Vasyl Turcheniuk² 

[1] Rivne State University of Humanities;National University of Water and Environmental Engineering

关键词: conformal mapping;    drainage systems;    filtration processes;    flood protection;    mathematical modelling;   

DOI  :  10.24425/jwld.2021.138163

学科分类：农业科学（综合）

来源: Instytut Technologiczno-Przyrodniczego / Institute of Technology and Life Sciences

【 摘 要 】

The article discusses the option for the application of the methodology for the solution of boundary value problems on the conformal mapping for the calculation of filtration process in the horizontal systematic drainage, provided that the drain is installed at a different depth. In particular, the case of methods combining fictitious areas and quasiconformal mappings for solving nonlinear boundary conditions problems for calculating filtration regimes in soils with free sections of boundaries (depression curves) and intervals of the “drainage” type. As an example, the authors designed a hydrodynamic flow grid, determined the values of the flows to the drain, established a section line and elicited other process characteristics. The algorithm for the numerical solution of model nonlinear boundary conditions problems of quasiconformal reflection in areas bounded by two equipotential lines and two flow lines, when for one of the sections, the boundary is an unknown (free) curve with fixed and free ends. The conducted numerical calculations prove that the problems and algorithms of their numerical solution, with a relatively small iterations number (k = 141) suggested in the paper, can be applied in the simulation of nonlinear filtration processes that arise in horizontal drainage systems. Total filtration flow obtained Q = 0.9 dm3·s–1; flow for drains Q1 = 0.55 dm3·s–1 and Q2 = 0.35 dm3·s–1 are quite consistent with practically determined values.

【 授权许可】

Unknown