LV    EN

Latvijas Zinātnes padomes Fundamentālo un lietišķo pētījumu programmas projekts

Šķidruma mehānikas un siltuma vadīšanas

sarežģīto dinamisko sistēmu analīze

Projekts ir veltīts vairāku nestacionāru problēmu fundamentāliem pētījumiem un to pielietojumiem siltuma vadīšanā un šķidruma mehānikā.

Projekta mērķis ir izstrādāt matemātiskos modeļus un algoritmus, lai pētītu trīs galveno problēmu grupas:

• faktoru, kas ietekmē efektīvo biomasas pārstrādi, tīras enerģijas ražošanu un atkritumu utilizāciju, analīze;

• siltuma vadīšanas un šķidruma mehānikas ātro nestacionāro procesu pētīšana (ieskaitot inverso uzdevumu risināšanu);

• vairāku siltuma vadīšanas režīmu analīze radiālās simetrijas gadījumā un atbilstošo nelineāro robežproblēmu atrisināmības, atrisinājumu sazarošanās un bifurkāciju pētīšana.

Sagaidāmie rezultāti ir šādi:

• izstrādāti matemātiskie modeļi, algoritmi un datorprogrammas, lai analizētu dinamiskās sistēmas, kas ir saistītas ar biomasas siltuma pārstrādi, tīras enerģijas ražošanu un atkritumu utilizāciju;

• siltuma vadīšanas nestacionāru procesu analīze un kontrole ar izstrādāto modeļu palīdzību, inverso nestacionāro hiperbolisko procesu atrisināšana (ar pielietojumiem tērauda rūdīšanā);

• pārējas uz turbulenci ātri palēnināto plūsmu caurulēs un kanālos analīze, izmantojot absolūtās un konvektīvās nestabilitātes jēdzienus;

• parasto diferenciālvienādojumu un to sistēmu nelineāro robežproblēmu analīzes jaunas metodes.

• 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 8-10, 2023.

• F. Sadyrbaev, Multiple heat conduction regimes and related nonlinear boundary value problems, 1st Sharjah International Conference on Mathematical Sciences (SICMS23), November 6-8, 2023, Sharjah, UAE.

• F. Sadyrbaev, Heat transfer regimes in nonlinear media, 2nd International Conference on Materials Science & Engineering, November 8-9, 2023, Dubai, UAE.

• F. Sadyrbaev, On differential equations with exponential nonlinearities, International Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP 2023), October 12-14, 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 11-17, 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 11-17, 2023, Heraclion, Crete, Greece.

• A. Kolyshkin, Weakly nonlinear instability of a convective flow due to non-homogeneous heat sources, 12th International conference on pure and applied mathematics (ICPAM 2023), July 18-21, 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 Multi-scale Computational Methods for Solids and Fluids (ECCOMAS MSF 2023), June 25-27, 2023, Sarajevo, Bosnia and Herzegovina. Proceedings.

• N. Budkina and A. Kolyshkin, Amplitude evolution equations for the analysis of non-isothermal 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 Ginzburg-Landau 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 Hydro-environment Engineering and Research (IAHR) World Congress, June 19-24, 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 5-9, 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, Non-standard method of solving direct and inverse problems for hyperbolic equations, 21st International Scientific Conference Engineering for Rural Development (ERDev2022), May 25-27, 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 21-22, 2022, Daugavpils, Latvia. Book of Abstracts.

• A. Gritsans, A. Kolyshkin, D. Ogorelova, F. Sadyrbaev, I. Samuilika, and I. Yermachenko, The application of the Krasnosel’skii-Guo 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 Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'21), June 24-29, 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 13-16, 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 26-28, 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 15-16, 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.

• 10.11.2023. Lietišķā matemātika jeb kā formula var uzlabot mūsu dzīvi. Raksts laikrakstā "Latgales Laiks".

• 29.09.2023. Matemātikas formulas = attīstība. Raksts laikrakstā "Latgales Laiks".

• 29.09.2023. 2023 Eiropas Zinātnieku nakts Daugavpils Universitātē. Programma.

• 15.05.2022. Informācija par projektu RTU Facebook grupā. [Ekrānuzņēmums.]

• 07.04.2021. Informācija par projekta vebināru RTU Facebook grupā. [Ekrānuzņēmums.]

• 11.03.2021. Informācija par projekta vebināru DU mājas lapā. [Ekrānuzņēmums.]

• 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 3-7, 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 8-10, 2023, Kraków, Poland), 2023, pp. 87-90. [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 Multi-scale Computational Methods for Solids and Fluids (ECCOMAS MSF 2023, June 25-27, 2023, Sarajevo, Bosnia and Herzegovina), 2023, pp. 160-163.

• 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 26-30, 2022, Funchal, Portugal), 2022, pp. 301-302.

• A. Kolyshkin, V. Koliskina, and I. Volodko, Stability of a convective flow generated by non-uniform heat sources in a transverse magnetic field, JP Journal of Heat and Mass Transfer, Vol. 29, 2022, pp. 105-123. [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 Hydro-environment Engineering and Research (IAHR) World Congress (June 19–24, Granada, Spain), 2022, pp. 1616-1624. [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. 151-160. [Scopus]

• T. Treilande and I. Iltins, Non-standard method of solving direct and inverse problems for hyperbolic equations, Proceedings of 21st International Scientific Conference "Engineering for Rural Development" (May 25-27, Jelgava, Latvia), 2022, pp. 383-888. [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. 305-335. [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 26-28, Jelgava, Latvia), 2021, pp. 837-842. [Scopus]

• F. Sadyrbaev, Multiple heat conduction regimes and related nonlinear boundary value problems, Abstracts of the 1st Sharjah International Conference on Mathematical Sciences  (November 6-8, 2023, Sharjah, UAE), 2023, p. 39.

• N. Budkina and A. Kolyshkin, Amplitude evolution equations for the analysis of non-isothermal 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 Ginzburg-Landau 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 5-9, 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 21-22, 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 15-16, 2021, Daugavpils, Latvia), 2021, p. 128.