Finite elements method in problems of lime lixiviation from the concrete bases of hydro technical constructions
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 79, Issue 3
Abstract
The ecological, economical and technogenic safety of the state and region is connected with the hydro–technical constructions operation fail-safety. One of the prediction methods, which does not need expensive experiments, is mathematical modeling. The non-linear mathematical model of the process of the lime lixiviation from the concrete bases of hydro–technical constructions was analysed. The non-linearity deals with taking into consideration the dependencies of the diffusion and water filtration coefficients on the salts concentration, as well as the chemical and thermal osmosis phenomenon, including thermal diffusion. The problem is of the Stephan’s type problems, as the corrosion border of the concrete basement is travelling. This contributes to the difficulties in finding the algorithms for of the approximate solutions for the relevant boundary problems. In the previous authors’ works for the finite differences method was used to solve these problems. But the precision of the approximate solutions was not reached. One of the ways to solve the problem is to compare the numerical solutions of the non-linear boundary problem, which were found using different similar methods. This is the aim of the article. As far as methods are concerned, the finite differences method and the finite elements method were chosen. The positive aspect in comparing this two methods is as follows – with the finite differences method we get the classical solution, and with the finite elements method – a generalized solution. One of the stages in achieving the final goal has been reached in this article – the scheme of approximate solution with the finite elements method is described. The program realization of the formed problem’s solution with the finite elements method has been realized in Lasarus – free software development environment for Free Pascal compiler. This integrated development environment provides an opportunity of cross platform creation of Delphi-like ads. The developed program allows changing the incoming data dynamically; controlling the area fragmentation and receiving the calculation results in graphical or numerical (in the table form) view.
Authors and Affiliations
Olga Stepanchenko, Petro Martinyuk
Keywords
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