Harijs Kalis

Harijs Kalis
University of Latvia | LU · Institute of Mathematics and Computer Science

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137
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Publications

Publications (137)
Article
In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP...
Article
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The main goal of the present study is to promote a more effective use of agriculture residues (straw) as an alternative renewable fuel for cleaner energy production with reduced greenhouse gas emissions. With the aim to improve the main combustion characteristics at thermo-chemical conversion of wheat straw, complex experimental study and mathematic...
Article
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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...
Article
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The aim of this study was to provide more effective use of straw for energy production by co-firing wheat straw pellets with solid fuels (wood, peat pellets) under additional electric control of the combustion characteristics at thermo-chemical conversion of fuel mixtures. Effects of the DC electric field on the main combustion characteristics were...
Article
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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...
Article
The main goal of the present study is to assure a more effective use of CO2 neutral fuel (wheat straw) for cleaner energy production with reduced greenhouse carbon emissions by partially replacing a fossil fuel (crashed coal) with a renewable one. This work combines experimental study and mathematical modelling of the processes developing during th...
Article
The main goal of the present study is to obtain a more effective utilization of wheat straw for energy production during a co-combustion with peat. For this purpose, an electric field was applied to the flame produced by the combustion of volatiles. This work combines experimental study and mathematical modelling of the processes developing during...
Article
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This paper deals with a simplified model taking into account the interplay of compressible, laminar, axisymmetric flow and the electrodynamical effects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxida...
Article
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Development of gyrotrons requires careful understanding of different regimes of gyrotron oscillations. For a long time, the gyrotron theory was developed assuming that the transit time of electrons through the interaction space is much shorter than the cavity fill time. Correspondingly, it was assumed that during this transit time, the amplitude of...
Article
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In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the tran...
Article
Full-text available
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...
Article
Full-text available
The present paper discusses a mathematical model of 3D compressible, laminar flame flow, considering the Lorentz force action on the development of fuel combustion in a cylindrical pipe. The combustion process is modelled with Arrhenius kinetics using two exothermic chemical reactions. A system of non-stationary partial differential equations with...
Article
In this paper 2D stationary boundary value problem for the system of magnetohy-drodynamic (MHD) equations along with the heat transfer equation is considered. The viscous electrically conducting incompressible liquid-electrolyte is to move between infinite cylinders placed periodically. Similarly 2D MHD channel flow with periodically placed obstacl...
Article
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Experimental studies and mathematical modelling of the effects of magnetic field on combustion dynamics at thermo-chemical conversion of biomass are carried out with the aim of providing control of the processes developing in the reaction zone of swirling flame. The joint research of the magnetic field effect on the combustion dynamics includes the...
Article
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We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coeffic...
Conference Paper
In this paper we consider 2D stationary boundary value problems for the system of magnetohydrodynamic (MHD) equations and the heat transfer equation. The viscous electrically conducting incompressible liquid moves between infinite cylinders with square or round sections placed periodically. We also consider similar 2D MHD channel flow with periodic...
Article
Mathematical modelling and numerical simulation of second-order reaction kinetics for fast and slow exothermic reactions has been applied with the aim to estimate the development of composition and temperature profiles downstream of the flame reaction zone. The effects of slow and fast exothermic reactions on the formation of the flame composition...
Article
Experimental study and mathematical modelling were aimed to provide electric control of biomass thermochemical conversion and analysis of the DC electric and electromagnetic effects on combustion dynamics to obtain a cleaner and a more effective heat energy production. Mathematical modelling of the formation of flame velocity and temperature profil...
Conference Paper
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In this paper we develop mathematical models for 2-D and 1-D hyperbolic heat equations (wave equation or telegraph equation) and construct their exact analytical solutions for the determination of the initial heat flux for rectangular samples. Some solutions of time inverse problems are obtained by Green function method as time inverse problems. Ap...
Article
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The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.
Article
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Bogs have been formed by an accumulation of peat -a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge's of peat metals content are i...
Article
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Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very l...
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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 fe...
Research
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11th ECMI Conference, Torre Normanna, Altavilla Milicia, Palermo- Italia, 26-30 September,2000.
Research
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ECMI 94, 8th Conference of the European Consortium for Mathematics in Industry. University of Kaiserslautern, Germany, September 6-10, 1994.
Research
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Abstracts of 12th Conference of the European Consortium for Mathematics in Industry. Jurmala, Latvia, September 10-14, 2002.
Research
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Abstracts of the 13th International Conference on Mathematical Modelling and Analysis, June 4- June 7, 2008.
Research
Abstracts of the 13th International Conference on Mathematical Modelling and Analysis, June 4- June 7, 2008.
Research
Abstracts of the 13th International Conference on Mathematical Modelling and Analysis, June 4- June 7, 2008.
Research
Full-text available
Abstracts of 12th Conference of the European Consortium for Mathematics in Indutry. Jurmala, Latvia, September 10-14, 2002.
Research
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WSEAS Transactions on Mathematics. Issue 4, Volume 6, April 2007.
Research
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WSEAS Transactions on Environment and Development, Issue 1, Volume 1, October 2005.
Research
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Abstracts of the International Conference Mathematical Modelling and Analysis, May 26-29, 2010.
Article
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Development of gyrotrons requires careful understanding of different regimes of gyrotron oscillations. It is known that in the planes of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current or cyclotron resonance mismatch and dimensionless interaction length complicated alternating sequences of regions of stati...
Article
Full-text available
Dynamics and hysteresis of an elongated droplet under the action of a rotating magnetic field is considered for mathematical modelling. The shape of droplet is found by regularization of the ill-posed initial–boundary value problem for nonlinear partial differential equation (PDE). It is shown that two methods of the regularization – introduction o...
Conference Paper
In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions (BCs) and periodic boundary conditions (PBCs) are studied. The finite difference scheme (FDS) and the finite difference scheme with exact spectrum (FDSES) are used for the space discretization. The solution in the time is obtained an...
Article
In many technological applications it is important to stir an electrically conducting liquid using various magnetic fields. The viscous electrically conducting incompressible liquid moves between infinite cylinders of square section placed periodically. We analyze a 2D flow around these cylinders subject to an external uniform magnetic field. The d...
Article
Full-text available
The gyrotron is a microwave source whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. Powerful gyrotrons can be used to heat nuclear fusion plasma. In addition, they have found a wide utility in plasma diagnostics, plasma chemistry, radars, extra-high-resolution spectroscopy, high-tem...
Article
Full-text available
Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order...
Article
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Dynamics of an elongated droplet under the action of a rotating magnetic field is considered by mathematical modelling. The actual shape of a droplet is obtained by solving the initial-boundary value problem of a nonlinear singularly perturbed partial differential equation (PDE). For the discretization in space the finite difference scheme (FDS) is...
Article
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A 2-D stationary boundary value-problem for the diffusion equation with piecewise constant coefficients in a multi-layered domain is considered. Homogeneous boundary conditions of the first kind or periodic boundary conditions are considered in the x direction. An analytical method for solving the problem of the above type is developed. This method...
Article
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This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third...
Article
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In this paper we formulate a model of superparamagnetic filaments with internal dissipative torques due to the action of a rotating magnetic field. It is shown that spirals are formed at both ends of the filament due to the action of the internal torques. These spirals propagate to the center of the filament and collide, forming a compact cluster t...
Article
We introduce the notion of finite difference schemes with exact spectrum (FDSES). We use these shemes for numerical solving ordinary differential equations and partial differential equations with boundary conditions of the first kind. We compare the results obtained by FDSES with the results obtained by other finite difference schemes. We prove sev...
Article
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The dynamics of magnetic laments under the action of dissipative torques is formulated in terms of the intrinsic variables of the curve - curvature and tension. The algorithm for the solution of the equations for the intrinsic variables is described and it is shown that the obtained results coincide with the results obtained by the explicit solutio...
Article
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There are considered some aspects for numerical solving of problem with Robin's boundary conditions arising in the gyrotron theory. The single mode case is carefully investigated. The obtained observations make possible to offer the suitable strategy for the numerical solving of the problem for general system of nonstationary gyrotron oscillations.
Conference Paper
Full-text available
The solutions of corresponding 1-D initial-boundary value problem and inverse problem for hyperbolic heat conduction equation are obtained numerically, using for the approach differential equations, the discretization in space applying the finite difference method and the best scheme with exact spectrum (BSES). Numerical solutions in the time are o...
Article
A viscous electrically conducting incompressible liquid is located between two infinite coaxial cylinders (rings), surfaces of which can rotate with different angular velocities. External magnetic fields (homogeneous, radial, axial, dipolar) are imposed. Distributions of electromagnetic forces and 2D magnetohydrodynamic flow induced by an external...
Article
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A stationary problem with the integral boundary condition arising in the mathematical modelling of a gyrotron is numerically investigated. The Chebyshev's polynomials of the second kind are used as the tool of calculations. The main result with physical meaning is the possibility to determine the maximal value of electrons efficiency. First publis...
Article
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The heating of buildings by ecologically clean and compact local devices is an interesting and actual problem. One of the modern areas of applications developed during last ten years is an effective usage of electrical energy by alternating current to produce heat energy. This work presents the mathematical model of one of such devices. It is a fin...
Article
We study the numerical methods for solving the initial-boundary value problems of some nonlinear heat transfer equations in multi-layer domain. The approximation of corresponding initial boundary value problems is based on the finite volume method (FVM), on the boundary element method (BEM), and on the finite-difference scheme (FDS). These methods...
Article
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The effective use of vortex energy in production of strong velocity fields by different devices is one of the modern areas of applications, developed during the last decade. In this paper the distribution of velocity field for viscous incompressible fluid in a pipe with a system of finite number of circular vortex lines, positioned on the inner sur...
Article
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The article features the system of three partial differential equations, which describes the stream stationary axial - a symmetric incompressible liquid in a pipe. The developed technique allows reduce the system of PDE to the difference equations which have been solved due to the grid method. Using computer program MAPLE different values of pressu...
Article
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We calculate the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of vortex threads in a finite cylinder, a finite trustum of the cone and channel. An original method is used to calculate the component of the velocity vectors. Such a procedure allows us to calculate the velocity field...
Article
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In this paper we study the problem of the diffusion of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. The transfer of moisture and the heat are described by the model. The system of two partial differential equations (PDEs) is derived, o...
Article
Full-text available
In this paper we calculate the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of vortex threads in a finite cylinder, in a finite frustum of the cone and in a channel. An original method was used to calculate the components of the velocity vectors. Such a procedure allows us to calcu...
Article
Full-text available
There are well-known different numerical methods for solving the boundary value problems for partial differential equations. Some of them are: finite difference method (FDM), finite element method (FEM), boundary element methods (BEM), and others. In the given work two methods FDM and BEM for the mathematical model of stationary distribution of hea...
Chapter
Numerical aspects for solving of certain problem arising in gyrotron theory are discussed. Particularly, finite-difference schemes using quasistationarization and method of lines were applied and the relevant results analyzed.
Article
Full-text available
In this paper we calculate the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of vortex threads in a finite frustum of the cone. An original method was used to calculate the radial and axial components of the velocity vectors. Such a procedure allows us to calculate the velocity fiel...
Article
Full-text available
The distribution of electromagnetic fields, forces and source term of temperature induced by an alternating axially-symmetric system of electric current in a cylinder of a finite length with 6 electrodes has been investigated and calculated in [2, 1]. In this paper the three-phase alternating current with phase shift 120 degree is fed to every of 9...
Article
The problem of Schrödinger equation with complex boundary conditions for modelling a motion of electrons in gyrotrons is considered. Numerical results obtained by using Fourier, Finite Differences (FD) and Degenerate Matrices (DM) methods are compared in the simplest case. For DM methods they are analysed also in more general cases, when FD can not...
Article
In this paper we study the simple algorithms for modelling the heat transfer problem in two layer media. The initial model which is based on a partial differential equation is reduced to ordinary differential equations (ODEs). The increase of accuracy is shown if instead of first order ODE initial value problem ([4, 5]) the second order differentia...
Article
We consider the simple algorithms in the modelling of the transfer problem of different substances (concentration, heat, moisture, and e. c.) in plate. The approximations of corresponding initial – boundary value problem of the system of the partial differential equations (PDE) is based on the finite volume method. This procedure allows one to redu...
Article
In this paper we study numerical problems arising in solving the single mode gyrotron equation. Using the method of finite differences analytical and numerical solutions are obtained. Quasistationary solutions and corresponding eigenvalues and eigenfunctions of this problem are investigated. Girotrono lygties vienos modos skaitiniai sprendimai Sa...