ENGINEERING GEOLOGY WORLD Vol. XVIII, No. 2/2023
Lekhov M.V.
Lekhov M.V., 2023. Finite element method in profile models of the seepage with a free surface. PERFIL software. Engineering Geology World, Vol. XVIII, No. 2, pp. 44–63, https://doi.org/10.25296/1993-5056-2023-18-2-44-63.
The paper contains a detailed mathematical formulation of the flow models intended for calculating two-dimensional seepage in a section. Engineering and hydrogeological studies in building design consider, as a rule, groundwater aquifers, to which flows with a free surface are confined. This is a special class of problems that require a special approach to schematization of hydrogeological conditions and mathematical formalization of models. Generalization of practical cases, analysis of typical schemes, and data necessary for calculations made it possible to develop a software simulation system that can be considered as universal for solving stationary and non-stationary problems of confined and unconfined seepage. The paper pays special attention to the schematization and consideration of various types of boundary conditions. The PERFIL simulation software contains the code for solving a differential equation using the finite element method. The paper presents the conclusion of the method in relation to calculations of flow in an aquifer with angular unconformity in the layers’ occurrence, leakage, and infiltration. Numerous factors of problems’ non-linearity, such as free surface, flooding of the earth’s surface, dewatering of drainage, and backwater of the reservoirs’ bed, determine the use of automated iterative search. The construction of the grid, setting of boundary conditions and parameters are carried out directly on the screen. Working with a tabular and graphical data editor is accompanied by rebuilding the model after entering each numerical parameter. Using the software does not require special theoretical knowledge of underground hydrodynamics and computational mathematics. The graphical grid designer and visual presentation of the results make it possible to use the software to familiarize students with profile models and to conduct practical exercises in the engineering hydrogeology training course.
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MIKHAIL V. LEKHOV
Lomonosov Moscow State University; Moscow, Russia; mvlekhov@geol.msu.ru
Address: Bld. 1, Leninskie Gory, 119991, Moscow, Russia