dario.bettoni said:Hi there, does any of you know a place where I can find the derivation of the hydrodynamic equations (navier stokes, etc) starting from interacting particles? I need this done in a pedantic way as I have to deal with the case in which the free streaming length is of the same order of the averaging box, which is not the case in standard textbooks.
Thanks,
Dario
The purpose of deriving hydrodynamic equations from interacting particles is to better understand the behavior and dynamics of fluids and gases. By studying the interactions between individual particles, we can gain insight into the larger-scale behavior of these substances and make accurate predictions about their movement and properties.
Hydrodynamic equations are derived using statistical mechanics and the principles of fluid mechanics. This involves analyzing the forces and interactions between individual particles and using mathematical models to describe their collective behavior on a macroscopic scale.
These equations have a wide range of applications in fields such as fluid dynamics, meteorology, and oceanography. They are used to model and predict the behavior of fluids and gases in various systems, including weather patterns, ocean currents, and industrial processes.
Yes, hydrodynamic equations can be applied to both classical and quantum systems. However, in quantum systems, additional factors such as quantum fluctuations and wave-particle duality must be taken into account in order to accurately describe the behavior of the particles.
One limitation of these equations is that they are based on simplifying assumptions and may not accurately describe highly complex or turbulent systems. Additionally, they may not be applicable on a microscopic scale, where quantum effects dominate. Other factors such as non-ideal behavior of particles or chemical reactions may also limit their accuracy in certain situations.