<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer 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 of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p>The special parabolic and exponential spline, which interpolation middle integral values of piece-wise smooth function, are considered. With the help of this splines is reduce the problems of mathematical physics in 3-D with piece-wise coefficients to respect one coordinate to problems for system of equations in 2-D. This procedure allows reduce the 3-D problem to a problem of 2-D and 1-D problems and the solution of the approximated problem is obtained analytically.</p><p>The solution of corresponding averaged 2-D initial-boundary value problem is obtained also numerically, using for approach differential equations the discretization in space applying the central differences. The approximation of the 2-D non-stationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.</p>
The European Union has placed competence-based teaching and competence-based education as one of its highly relevant goals. Due to mass higher education, the assessment of effectiveness and relevance evaluation of environmental engineering study programmes should become an important issue. Presently the focus of the evaluation on multi-disciplinary study programmes varies from the evaluation of attitudes, impacts or effectiveness of utilisation-focused evaluation, summative evaluation and participatory evaluation approaches. The objective of this study was to propose an effective framework to evaluate the Environmental Engineering Master study programmes. During the research, the evaluation of existing study programmes on environmental engineering in Europe was conducted, information about the study courses, teaching methods, assessment methods and competences was used for the analysis. The results obtained showed that lectures, site visits, group coursework, practical laboratories and role-plays allows to reach the necessary knowledge, skills and competences and to provide an effective and relevant education to the Environmental Engineering Master programme students. The proposed evaluation framework was tested and approbated on new Riga Technical University Master study programmes on Environmental Engineering and Bioeconomy.
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.Keywords: 3-D boundary-value problem, averaging method, finite difference method, heavy metals Fe and Ca, peat bog.
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