Abstract
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodical boundary condition in x direction. This procedure allows to reduce the 3-D problem to a system of 2-D problems by using circulant matrix.
Highlights
Peat is a mixture of plant remains in different stages of decay consisting in five main groups of organic compounds: proteins, lipids, hydrocarbons, pigments and lignin [11].Regional climate, the nature of the vegetation, water pH, and degree of metamorphosis may affect the characteristics of the peat [1].Trace elements accumulated in peat lands have two main natural sources [11]: 1) Atmospheric deposition of soil dusts and aerosols; 2) The incorporation as particulate matter or in solution via runoff and ground waters
At trace levels some heavy metals are essential for plants and animals, at higher concentrations they become dangerous for any form of life [10]
Mathematical models which based on real measurements are more reasonable to use for practical estimation of necessary elements of other required points of peat layers
Summary
Peat is a mixture of plant remains in different stages of decay consisting in five main groups of organic compounds: proteins, lipids, hydrocarbons, pigments and lignin [11]. Trace elements accumulated in peat lands have two main natural sources [11]: 1) Atmospheric deposition of soil dusts and aerosols; 2) The incorporation as particulate matter or in solution via runoff and ground waters (by mineral dissolution or desorption of compounds previously accumulated in the environment). Main anthropogenic pollution sources are atmospheric particles, waste waters, results of changes in environmental conditions such as changes in pH value [11]. At trace levels some heavy metals are essential for plants and animals, at higher concentrations they become dangerous for any form of life [10]. Mathematical models which based on real measurements (which were made more accessible locations, for example, on the earth surface, or between layers of peat and with the minimum required number of measurements) are more reasonable to use for practical estimation of necessary elements of other required points of peat layers
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