- Teirumnieka, Ērika

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# Teirumnieka, Ērika

Preferred name

Teirumnieka, Ērika

Official Name

Teirumnieka, Ērika

Alternative Name

Ērika Teirumnieka

Erika Teirumnieka

Teirumnieka, Erika

Email

erika.teirumnieka@rta.lv

ORCID

Scopus Author ID

56323862400

Researcher ID

EBG-0589-2022

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- PublicationON MATHEMATICAL MODELLING OF THE 2-D FILTRATION PROBLEM IN POROUS AXIAL SYMMETRICAL CYLINDER(2017)
; ;Harijs Kalis; Show more In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs). One equation is expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetically equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axis-symmetrical mass transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.Show more - PublicationSPECIAL HPERBOLIC TYPE APPROXIMATION FOR SOLVING OF 3-D TWO LAYER STATIONARY DIFFUSION PROBLEM(2019)
; ;Harijs Kalis; Show more In this paper we examine the conservative averaging method (CAM) along the vertical z-coordinate for solving the 3-D boundary-value 2 layers diffusion problem. The special parabolic and hyperbolic type approximation (splines), that interpolate the middle integral values of piece-wise smooth function, is investigated. With the help of these splines the problems of mathematical physics in 3-D with respect to one coordinate are reduced to problems for system of equations in 2-D in every layer. This procedure allows reduce also the 2-D problem to a 1-D problem and the solution of the approximated problem can be obtained analytically. As the practical application of the created mathematical model, we are studying the calculation of the concentration of heavy metal calcium (Ca) in a two-layer peat block.Show more Scopus© Citations 1 - PublicationThe analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers(2015)
; ; ; Harijs KalisShow more 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. 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. 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.Show more Scopus© Citations 3