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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.

• M.Y Lam, A. Kolyshkin, and M.S. Ghidaoui, Initial dynamics responsible for wave radiation in shallow shear flows, 39th IAHR World Congress, June 19-24, 2022, Granada, Spain.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 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. Kolyshkin, V. Koliskina, and I. Volodko, Stability of a convective flow generated by non-uniform heat sources in a transverse magnetic field, submitted for publication to JP Journal of Heat and Mass Transfer on February 16, 2022, 15 pages. (Currently under the first revision).

• 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 IAHR World Congress (June 19–24, Granada, Spain), 2022, 9 pages. (Accepted for publication).

• 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.

• 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.

• 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.

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

• 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.

• 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.