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| Project title: | Analysis of complex dynamical systems in fluid mechanics and heat transfer |
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| Project short title: | CompDyn |
| Number of project implementation agreement: | lzp-2020/1-0076 |
| Registration number: | 4398 |
| Department: | Institute of Applied Mathematics |
| Administrating department: | Institute of Applied Mathematics |
| Finance fund: | LZP fundamentālo un lietišķo pētījumu projekts |
| Project RTU role: | leading partner |
| Status: | Ended |
| Project start date: | 01.01.2021. |
| Project end date: | 31.12.2023. |
| Title of grant issuer: | Latvijas Zinātnes padome |
| General manager: | Andrejs Koliškins |
| Administrative manager: | Anna Starikova |
| Project website: | www.de.du.lv/lzp2021 |
| Total finance: | |
| Projekta kopējais finansējums ir 300 000.00 EUR | |
| Summary: | |
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The project is devoted to the fundamental research of several non-stationary problems and their applications in heat conduction and fluid mechanics. The aim of the project is to develop mathematical models and algorithms to study three main groups of problems: (a) analysis of factors affecting efficient biomass processing, clean energy production and waste disposal; (b) study of fast non-stationary processes of heat conduction and fluid mechanics (including solving inverse problems); (c) analysis of several heat conduction regimes in case of radial symmetry and study of solvability, branching and bifurcations of the corresponding nonlinear boundary value problems. The expected results are as follows: developed mathematical models, algorithms and computer programs to analyze dynamic systems related to biomass heat processing, clean energy production and waste utilization; analysis and control of non-stationary processes of heat conduction with the help of developed models, solving of inverse non-stationary hyperbolic processes (with applications in steel hardening); analysis of the transition to turbulence of rapidly decelerated flows in pipes and channels using the concepts of absolute and convective instability; new methods of analysis of nonlinear boundary value problems of ordinary differential equations and their systems. |
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| Activities: | |
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Planned tasks: 1. Analysis of linear stability of fluid flow in a channel with heat sources and temperature difference between the wall. 2. Modeling the temperature field in landfills. 3. The influence of the magnetic field on the convective stability of the flow in the region between two vertical planes. 4. Influence of radial flow on the convective stability of the fluid in the area between two concentric cylinders under the condition that the convection is caused by nonlinear heat sources. 5. Weakly nonlinear stability analysis in the region between two vertical planes. 6. Solution of direct and inverse problemns for hyperbolic equations. 7. Convective instability of a fluid due to concentration heat sources. 8. Weakly nonlinear analysis of convective flows in Cartesian and cylindrical cooridnates. 9. Analysis of nonlinear boundary value problems for ordinary differential equations (existence and uniqueness of solutions, bifurcation analysis). 10. Unsteady flow analysis (absolute and convective instability). |
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| Project published on RTU website: | 01.01.2021. |