LV
EN 


Fundamental and applied
research project of the Latvian Council of Science 

Analysis of complex dynamical systems
in fluid
mechanics and heat transfer 


About project
Project summary
Research
group 
Conferences
Publicity 
Publications: Journals and Conference Proceedings 
Publications: Conference Abstracts 

About project


Project title: 
Analysis of complex dynamical systems in fluid mechanics and
heat transfer 

Project number: 
lzp2020/10076 

Project applicant: 
Riga Technical University 

Project cooperation partner: 
Daugavpils University 

Project science field: 
Mathematics 

Type of research: 
Fundamental research 

Project leader: 
Andrei Kolyshkin [Andrejs.Koliskins@rtu.lv] 

DU
project coordinator: 
Armands Gritsans
[armands.gricans@du.lv]


Project implementation period: 
01.01.2021.31.12.2023.

Project
summary

The project is devoted to fundamental
research of different types of unsteady phenomena with broad range of
applications in fluid mechanics and heat transfer.
The main objective of the project is to
develop mathematical models and algorithms to study the following three
groups of problems:

analysis of factors contributing to efficient
biomass thermal conversion, clean energy production and utilization of waste;

investigation of fast transient processes in
heat transfer and fluid mechanics (including solution of inverse problems);

analysis of multiple heat conduction regimes
in presence of radial symmetry and investigation of related nonlinear
boundary value problems, their solvability, branching of solutions, and
bifurcations.
The expected results are as
follows:

developed mathematical models, algorithms and
computer programs to analyze dynamic systems related to biomass thermal
conversion, clean energy production and utilization of waste;

use of developed models for analysis and
control of unsteady processes in heat transfer, solution of inverse
timedependent hyperbolic processes (with applications in steel quenching);

analysis of fast transient flows in pipes and
channels based on the notions of absolute and convective instability;

new methods of analysis of nonlinear boundary
problems for ordinary differential equations and their systems.

Research group


Riga Technical University:



Andrei Kolyshkin 
Dr.math., professor 

Mohamed Ghidaoui 
PhD, professor 

Inta Volodko 
Dr.math., professor 

Ilmārs Iltiņš 
Dr.sc.ing., professor 

Marija Iltiņa 
Dr.sc.ing., associate professor 

Valentīna Koliškina 
Dr.math., docent 

Maksims Žigunovs 
Mg.sc.ing. 

Daugavpils University:



Armands Gritsans 
Dr.math, associate professor 

Felix Sadyrbaev 
Dr.habil.math, professor 

Inara Yermachenko 
Dr.math, associate professor 

Diāna Ogorelova 
Mg.math. 

Inna Samuilika 
Mg.math. 

Olga Kozlovska 
Mg.math. 
Conferences


V. Koliskina and A.
Kolyshkin, Stability of a decelerated flow in a plane channel,
8th International conference on mechanical
engineering and robotics research (ICMERR 2023), virtual
conference hosted by AGH University of Science and
Technology in Kraków (Poland), December
810, 2023.

F. Sadyrbaev, Multiple
heat conduction regimes and related nonlinear boundary value problems,
1st Sharjah International Conference on
Mathematical Sciences (SICMS23), November 68, 2023,
Sharjah, UAE.

F. Sadyrbaev, Heat
transfer regimes in nonlinear media,
2nd International Conference on Materials Science
& Engineering, November 89, 2023, Dubai, UAE.

F. Sadyrbaev, On
differential equations with exponential
nonlinearities,
International Workshop on Analysis and Numerical
Approximation of Singular Problems (IWANASP 2023),
October 1214, 2023, Régua, Portugal.

V. Koliskina and A.
Kolyshkin, On the instability of rapidly decelerated channel flows,
21st International Conference of Numerical
Analysis and Applied Mathematics (ICNAAM 2023),
September 1117, 2023, Heraclion, Crete, Greece.

V. Koliskina, A.
Kolyshkin, and I. Volodko, On the stability of a convective motion of a
mixture with concentration heat sources,
21st International Conference of Numerical
Analysis and Applied Mathematics (ICNAAM 2023),
September 1117, 2023, Heraclion, Crete, Greece.

A.
Kolyshkin, Weakly nonlinear instability of a convective flow due
to nonhomogeneous heat sources,
12th International conference on pure and applied
mathematics (ICPAM 2023), July 1821, 2023,
Polytechnic University of Porto, Portugal.

N. Budkina and A.
Kolyshkin, Weakly nonlinear instability of a convective flow caused by
internal heat generation,
6th International Conference on Multiscale
Computational Methods for Solids and Fluids
(ECCOMAS MSF 2023), June 2527, 2023, Sarajevo, Bosnia
and Herzegovina.
Proceedings.

N. Budkina and A.
Kolyshkin, Amplitude evolution equations for the analysis of
nonisothermal incompressible flows,
26th International Conference Mathematical
Modelling and Analysis, May 30  June 2, 2023,
Jurmala, Latvia.
Book of Abstracts.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, Linear stability of a
combined convective flow in an annulus,
26th International Conference Mathematical
Modelling and Analysis, May 30  June 2, 2023,
Jurmala, Latvia.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
Multiplicity results for boundary value
problems with the Arrhenius nonlinearity,
26th International Conference Mathematical
Modelling and Analysis May 30  June 2, 2023, Jurmala,
Latvia.
Book of Abstracts.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Stability of a steady convective flow in a
vertical channel with permeable boundaries,
26th International Conference Mathematical
Modelling and Analysis, May 30  June 2, 2023,
Jurmala, Latvia.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
On the multiplicity of solutions for a boundary value problem
with the Arrhenius nonlinearity,
65th International Scientific Conference of
Daugavpils University, April 20  21, 2023,
Daugavpils, Latvia.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
On a boundary value problem with the Arrhenius nonlinearity,
81st International Scientific Conference of the
University of Latvia, February 24,
2023, Riga, Latvia.
Book of Abstracts.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Stability of a convective flow due to
internal heat sources in a magnetic field,
XII International conference of the Georgian
Mathematical Union, August
29  September 3, 2022, Batumi, Georgia.
Book of Abstracts.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Thermal convection in an
annulus: a linear stability analysis,
XII International conference of the Georgian
Mathematical Union, August
29  September 3, 2022, Batumi, Georgia.
Book of Abstracts.

N. Budkina and A.
Kolyshkin, Derivation of the GinzburgLandau equation for a convective
flow in a vertical fluid layer,
XII International conference of the Georgian
Mathematical Union, August
29  September 3, 2022, Batumi, Georgia.
Book of Abstracts.

M.Y Lam, A.
Kolyshkin,
and M.S. Ghidaoui, Initial dynamics
responsible for wave radiation in shallow shear flows,
39th International Association for
Hydroenvironment Engineering and Research (IAHR) World Congress, June 1924, 2022, Granada, Spain.
Abstract.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, Instability of a flow of a
reacting fluid in a vertical fluid layer,
8th European Congress on Computational Methods in
Applied Sciences and Engineering (ECCOMAS CONGRESS 2022),
June 59, 2022, Oslo, Norway.
Abstract.

V. Koliskina,
A.
Kolyshkin, and M. Zigunovs, Stability of convective
flows caused by internal heating,
25th International Conference Mathematical
Modelling and Analysis, May 30  June 2, 2022, Druskininkai, Lithuania.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
On a nonlinear boundary value problem arising in heat transfer,
25th International Conference Mathematical
Modelling and Analysis, May 30  June 2, 2022, Druskininkai, Lithuania.
Book of Abstracts.

T. Treilande and I.
Iltins, Nonstandard method of solving direct and inverse problems for
hyperbolic equations,
21st International Scientific Conference
Engineering for Rural Development (ERDev2022),
May 2527,
2022, Jelgava, Latvia.
Proceedings.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
Multiplicity of positive solutions for a boundary value problem arising
in heat transfer,
64th International Scientific Conference of
Daugavpils University, April 2122, 2022, Daugavpils,
Latvia.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
The application of the Krasnosel’skiiGuo fixed point theorem to a
boundary value problem arising in heat transfer,
80th International Scientific Conference of the
University of Latvia, February 25,
2022, Riga,
Latvia.

V. Koliskina, A.
Kolyshkin, and I. Volodko,
Stability of combined steady convective flow in a vertical fluid layer
with permeable boundaries,
13th Conference of the EuroAmerican Consortium
for Promoting the Application of Mathematics in Technical and Natural
Sciences (AMiTaNS'21), June 2429, 2021, Albena,
Bulgaria.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, On the stability of a steady
convective flow in a vertical layer of a chemically reacting fluid,
9th International Conference on Computational
Methods for Coupled Problems in Science and Engineering (COUPLED
PROBLEMS 2021), June 1316, 2021.
Proceedings.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
Solutions of nonlinear boundary value problem with applications to
biomass thermal conversion,
20th International Scientific Conference
Engineering for Rural Development (ERDev2021), May 2628,
2021, Jelgava, Latvia.
Proceedings.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
On a Dirichlet problem for second order nonlinear nonautonomous ordinary
differential equations,
63rd International Scientific Conference of
Daugavpils University, April 1516, 2021, Daugavpils,
Latvia.
Book of Abstracts.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
On some nonlinear boundary values problems for ordinary differential
equations in heat conduction theory,
79th International Scientific
Conference of the University of Latvia, February 26, 2021, Riga,
Latvia.

A. Gritsans, A.
Kolyshkin, and F. Sadyrbaev, Stability of convective flows in the presence
of nonlinear heat source,
79th International Scientific
Conference of the University of Latvia, February 26, 2021, Riga, Latvia.

Publicity


Publications: Journals and
Conference Proceedings


A. Gritsans, A.
Kolyshkin, F. Sadyrbaev, and I. Yermachenko,
Effect of rotation of the boundaries on the stability of a flow caused
by a nonlinear heat source, submitted for presentation and possible
publication at
the 9th European Congress on Computational Methods
in Applied Sciences and Engineering (ECCOMAS 2024), June 37,
2024, Lisbon, Portugal.

V. Koliskina and A.
Kolyshkin, Stability of a decelerated flow in a plane channel,
Proceedings of the 8th International conference on
mechanical engineering and robotics research (December 810, 2023,
Kraków, Poland), 2023, pp. 8790.
[Scopus]

A. Gritsans, A.
Kolyshkin, F. Sadyrbaev, and I. Yermachenko, On the stability of a
convective flow with nonlinear heat sources,
Mathematics, 11(18): 3895, 2023.
[Scopus]

N. Budkina and A.
Kolyshkin, Weakly nonlinear instability of a convective flow caused by
internal heat generation,
Proceedinds of 6th International Conference on
Multiscale Computational Methods for Solids
and Fluids (ECCOMAS MSF 2023, June 2527, 2023, Sarajevo, Bosnia and
Herzegovina), 2023, pp. 160163.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev,
Linear stability of a combined convective flow in an annulus,
Fluids, 8(4):130, 2023.
[Scopus]

M. Zigunovs
and A. Kolyshkin, The effect of the
Prandtl number on the stability of a convective flow with permeable
walls,
Proceedings of the 9th International conference on
mechanics and materials in design (June 2630, 2022, Funchal, Portugal),
2022, pp. 301302.

A. Kolyshkin,
V. Koliskina, and I. Volodko, Stability of a
convective flow generated by nonuniform heat sources in a transverse
magnetic field,
JP Journal of Heat and Mass
Transfer, Vol.
29, 2022, pp.
105123. [Scopus]

A. Kolyshkin, V.
Koliskina, and I. Volodko, Stability of combined steady convective flow
in a vertical fluid layer with permeable boundaries,
AIP Conference Proceedings, Vol. 2522,
080003, 2022, 7 pp.
[Scopus]

M.Y. Lam, A. Kolyshkin,
and M.S. Ghidaoui, Initial dynamics
responsible for the stabilizing effect of Froude number in shallow shear
flows,
Proceedings of the 39th International Association
for Hydroenvironment Engineering and Research (IAHR) World Congress
(June 19–24, Granada, Spain), 2022,
pp. 16161624.
[Scopus]

I. Samuilik and F.
Sadyrbaev, On a system without critical points arising in heat
conductivity theory,
WSEAS Transactions on
Heat and Mass Transfer, 2022, 17,
pp. 151160. [Scopus]

T. Treilande and I.
Iltins, Nonstandard method of solving direct and inverse problems for
hyperbolic equations,
Proceedings of 21st International Scientific
Conference "Engineering for Rural Development" (May 2527, Jelgava,
Latvia), 2022, pp. 383888.
[Scopus]

M. Zigunovs, I. Iltins,
and M. Iltina, Fluid driven thermal distribution in porous media
applying parallel calculations,
JP Journal of Heat and Mass Transfer,
22(2), 2021, pp. 305335.
[Scopus]

M. Zigunovs, A.
Kolyshkin, and I. Iltins, Linear stability of a steady convective flow
between permeable cylinders,
Fluids, 6(10):342, 2021.
[Scopus]

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, On
the stability of a steady convective flow in a vertical layer of a
chemically reacting fluid, in:
9th edition of the International Conference on
Computational Methods for Coupled Problems in Science and Engineering
(COUPLED PROBLEMS 2021), Vol. IS34  Multiphysics Problems, 2021,
10 pp.
[Scopus]

A. Gritsans,
A. Kolyshkin, D. Ogorelova,
F. Sadyrbaev, I. Samuilik, and
I. Yermachenko, Solutions of nonlinear boundary value problem
with applications to biomass thermal conversion,
Proceedings of 20th International Scientific
Conference "Engineering for Rural Development" (May 2628, Jelgava,
Latvia), 2021, pp. 837842.
[Scopus]

Publications: Conference
Abstracts


F. Sadyrbaev, Multiple
heat conduction regimes and related nonlinear boundary value problems,
Abstracts of the 1st Sharjah International
Conference on Mathematical Sciences (November
68, 2023, Sharjah, UAE), 2023, p. 39.

N. Budkina and A.
Kolyshkin, Amplitude evolution equations for the analysis of
nonisothermal incompressible flows,
Abstracts of the 26th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2023, Jurmala,
Latvia), 2023,
p. 8.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, Linear stability of a
combined convective flow in an annulus,
Abstracts of the 26th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2023, Jurmala,
Latvia), 2023,
p. 17.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
Multiplicity results for boundary value problems with the Arrhenius
nonlinearity,
Abstracts of the 26th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2023, Jurmala,
Latvia), 2023,
p. 18.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Stability of a steady convective flow in a
vertical channel with permeable boundaries,
Abstracts of the 26th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2023, Jurmala,
Latvia), 2023,
p. 29.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
On the multiplicity of solutions for a boundary value problem with the
Arrhenius nonlinearity,
Abstracts of the 65th International Scientific
Conference of Daugavpils University, (April 20  21, 2023, Daugavpils,
Latvia), 2023, p. 87.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Stability of a convective flow due to
internal heat sources in a magnetic field,
Book of Abstracts of XII International conference
of the Georgian Mathematical Union (August 29  September 3, 2022,
Batumi, Georgia), 2022, p.
145.

V. Koliskina, A.
Kolyshkin, and I. Volodko, Thermal convection in an annulus: a linear
stability analysis,
Book of Abstracts of XII International conference
of the Georgian Mathematical Union (August 29  September 3, 2022,
Batumi, Georgia), 2022, p.
146.

N. Budkina and A.
Kolyshkin, Derivation of the GinzburgLandau equation for a convective
flow in a vertical fluid layer,
Book of Abstracts of XII International conference
of the Georgian Mathematical Union (August 29  September 3, 2022,
Batumi, Georgia), 2022, p.
80.

A. Gritsans, V.
Koliskina, A. Kolyshkin, and F. Sadyrbaev, Instability of a flow of a
reacting fluid in a vertical fluid layer,
The 8th European Congress on Computational Methods
in Applied Sciences and Engineering (June 59, 2022, Oslo, Norway), 2022.

V. Koliskina, A.
Kolyshkin, and M. Zigunovs, Stability of convective flows caused by
internal heating,
Abstracts of the 25th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2022,
Druskininkai, Lithuania), 2022,
p. 6.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
On a nonlinear boundary value problem arising in heat transfer,
Abstracts of the 25th International Conference
Mathematical Modelling and Analysis (May 30  June 2, 2022,
Druskininkai, Lithuania), 2022,
p. 4.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilik, and I. Yermachenko,
Multiplicity of positive solutions for a boundary value problem arising
in heat transfer,
Abstracts of the 64th International Scientific
Conference of Daugavpils University (April 2122, 2022, Daugavpils,
Latvia), 2022,
p. 91.

A. Gritsans, A.
Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko,
On a Dirichlet problem for second order nonlinear nonautonomous ordinary
differential equations,
Abstracts of the 63rd International Scientific
Conference of Daugavpils University (April 1516, 2021, Daugavpils,
Latvia), 2021,
p. 128.



