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Analysis of solution properties for the micropolar real gas flow problem

Natural Sciences/uniri young scientists projects 2022

The model of compressible real micropolar fluid flow was first considered in 2021 as a generalization of an idealized compressible microcontinuum. Several significant results on the existence and uniqueness of the model solution have been published and the corresponding numerical scheme has been constructed, but many of its properties are still unexplored. Angela Bašić-Šiško, together with collaborators from the Department of Applied Mathematics and Physics at the Faculty of Engineering, has begun research on this model as part of her dissertation, and this project enables its continuation. The model, which is the subject of this project, was created by updating classical ideas with the aim of combining the advantages of the known generalizations of the continuum and the equation of state. The micropolar model has proved extremely useful in describing the behavior of fluids with pronounced particle structure in microtubes, while the model of the real gas allows a departure from idealized assumptions that may deviate significantly from the actual state of the system, especially under extreme conditions. The generalized model is therefore an ideal framework for studying the behavior of gasses during combustion. This inspired its application to the reactive fluid model. As part of the project, it is planned to continue research into a one-dimensional model of a real micropolar gas flow and its application to the flow and thermal explosion model of a reactive fluid by testing the long-term behavior, stabilization and regularity of the solution. Indeed, so far, solutions have been shown to exist in a generalized sense only for a finite time. The focus of the proposed research is the existence of a solution in an infinite time interval, its stabilization around a stationary solution for large times, and additional smoothness. These results are consistent with the physical interpretation of the model and their validation would further confirm the validity of the model.