SIMPLE METHODS OF ENGINEERING CALCULATIONS FOR SOLVING TRANSFER PROBLEMS OF MULTI – SUBSTANCES IN HORIZONTAL LAYER

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 reduce the 2-D transfer problem described by a PDE to initial value problem for a system of ordinary differential equations (ODE) of the first or second order. In the stationary case the exact finite – difference vector scheme is obtained.

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SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN

Mathematical Modelling and Analysis ◽

10.3846/13926292.2017.1318796 ◽

2017 ◽

Vol 22 (4) ◽

pp. 425-440

Author(s):

Harijs Kalis ◽

Andris Buikis ◽

Aivars Aboltins ◽

Ilmars Kangro

Keyword(s):

Differential Equations ◽

Transfer Problem ◽

Circular Cross Section ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Rate Of Change ◽

Wood Block ◽

Initial Value ◽

Special Integral ◽

Initial Boundary Value

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 transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM) with special integral splines. This procedure allows reduce the 3-D axis-symmetrical transfer problem in multi-layered domain described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

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CALCULATION OF HEAT AND MOISTURE DISTRIBUTION IN THE POROUS MEDIA LAYER

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2007.12.91-100 ◽

2007 ◽

Vol 12 (1) ◽

pp. 91-100 ◽

Cited By ~ 2

Author(s):

Harijs Kalis ◽

Ilmars Kangro

Keyword(s):

Differential Equations ◽

Transfer Problem ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Rate Of Change ◽

Moisture Distribution ◽

Initial Boundary Value ◽

Volume Method ◽

Heat And Moisture ◽

Media Layer

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, one equation expresses the rate of change of concentration of water vapour in the air spaces and the other the rate of change of temperature. The obtained initial‐boundary value problem is approximated by using the finite volume method. This procedure allows us to reduce the 2D transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

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ON MATHEMATICAL MODELLING OF THE 2-D FILTRATION PROBLEM IN POROUS AXIAL SYMMETRICAL CYLINDER

Environment Technology Resources Proceedings of the International Scientific and Practical Conference ◽

10.17770/etr2017vol3.2566 ◽

2017 ◽

Vol 3 ◽

pp. 129

Author(s):

Ilmārs Kangro ◽

Harijs Kalis ◽

Ērika Teirumnieka ◽

Edmunds Teirumnieks

Keyword(s):

Differential Equations ◽

Transfer Problem ◽

Initial Boundary ◽

Axial Direction ◽

Initial Boundary Value Problem ◽

Rate Of Change ◽

Filtration Problem ◽

Dirty Water ◽

Round Cylinder ◽

Initial Boundary Value

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.

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ON MATHEMATICAL MODELLING OF THE SOLID-LIQUID MIXTURES TRANSPORT IN POROUS AXIAL-SYMMETRICAL CONTAINER WITH HENRY AND LANGMUIR SORPTION KINETICS

Mathematical Modelling and Analysis ◽

10.3846/mma.2018.033 ◽

2018 ◽

Vol 23 (4) ◽

pp. 554-567 ◽

Cited By ~ 3

Author(s):

Ilmars Kangroa ◽

Harijs Kalis

Keyword(s):

Differential Equations ◽

Transfer Problem ◽

Initial Boundary ◽

Axial Direction ◽

Initial Boundary Value Problem ◽

Liquid Mixtures ◽

Sorption Kinetics ◽

Rate Of Change ◽

Filtration Problem ◽

Initial Boundary Value

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 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 kinetical 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 axisymmetrical mass transfer problem decribed by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order. We consider also model 1-D problem for investigation the depending the concentration of water and sorbent on the time.

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SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM

Environment Technology Resources Proceedings of the International Scientific and Practical Conference ◽

10.17770/etr2021vol2.6577 ◽

2021 ◽

Vol 2 ◽

pp. 69-73

Author(s):

Ilmārs Kangro ◽

Harijs Kalis ◽

Ērika Teirumnieka ◽

Edmunds Teirumnieks

Keyword(s):

Mass Transfer ◽

Transfer Problem ◽

Spline Approximation ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Fourier Series Method ◽

Mass Transfer Problem ◽

Mass And Heat Transfer ◽

Initial Boundary Value ◽

Transfer Problems

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) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.

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On global dynamics of 2D convective Cahn–Hilliard equation

Boundary Value Problems ◽

10.1186/s13661-020-01477-3 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Xiaopeng Zhao

Keyword(s):

Initial Boundary ◽

Initial Boundary Value Problem ◽

Global Dynamics ◽

Time Behavior ◽

Long Time Behavior ◽

Initial Value ◽

Hilliard Equation ◽

Long Time ◽

Cahn Hilliard Equation ◽

Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

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DYNAMICS OF MULTISECTION SEMICONDUCTOR LASERS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2004.9637241 ◽

2005 ◽

Vol 9 (1) ◽

pp. 51-66 ◽

Cited By ~ 4

Author(s):

J. Sieber ◽

M. Radžiūnas ◽

K. R. Schneider

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Semiconductor Lasers ◽

Invariant Manifolds ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Low Dimension ◽

Global Existence And Uniqueness ◽

Numerical Bifurcation ◽

Initial Boundary Value

We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two-mode approximation system and compare it with the simulated dynamics of the full PDE model.

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