Modeling Turbulent Flows Through the Adaptive Wavelet Collocations Methods

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Professor O.V. Vasilyev suggested a simple and reliable method for solving hyperbolic equations, based on the wavelet collocations method and dynamically adaptive grid. It allows describing various physical phenomena and creating mathematical and computer models ensuring high calculation accuracy with the minimum power requirements to computation systems.


Modeling Turbulent Flows


It's widely known that there are two fluid flow patterns: laminar (sustainable, with the rectilinear motion of particles) and turbulent (fluid layers are mixing). Modeling laminar flows is not a difficult task as the majority of physical values describing the flow state can be calculated by simple formulas. In the turbulent mode, fluid particles move longitudinally and transversely—causing higher flow energy loss, increased heat exchange, and more complex velocity profile.


Even today, modeling turbulent fluid flows is an extremely difficult task requiring multiple calculations and high-performing computation equipment. The problem is turbulence is still considered a physical phenomenon of outstanding complexity behavior of which can be barely mathematically described.


Professor O.V. Vasilyev suggested a model of two-dimensional turbulence with the scaling of time-space modes based on the Reynolds number value which characterizes the flow type and speed at which fluid particles move. This innovative approach allows designing simplified models of turbulent medium flows, even in composite-section channels. It helps minimize the computation error probability thanks to using the adaptive spatial grid.


Practical Use


In engineering, most calculations consider turbulent fluid motion. O.V. Vasilyev's research is going to have a significant impact on different facets as the turbulent motion of fluid media is a common phenomenon.


Turbulence is observed in the human lungs and cardiovascular system. To this end, Professor O.V. Vasilyev's studies are highly valuable to healthcare—particularly, in the field of developing biological systems.


A fresh approach to modeling turbulent flows of media will have a profound effect on the development of various industrial sectors: chemical industry, oil-and-gas industry, machine engineering (hydraulic mechanisms), automotive industry, shipbuilding, etc. Using accurate simplified turbulence models will contribute to enhancing the efficiency of various production processes. It is also supposed to lead to a significant economic effect reflected in lower costs for end users—this is because the costs related to designing and modeling systems with turbulent flow of media will significantly decrease.


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