This is the second part in a series about Computational Fluid Dynamics where we build a Fluid Simulator from scratch.

We derive the Macroscopic Perspective (Continuum) from the Microscopic Perspective (Molecules) covering: Collective Molecular Behavior, Local (Non)Equilibria, Classical Statistical Mechanics, Rarefied Gas Dynamics, and Continuum Gas Dynamics.

The Macroscopic Perspective provides the ground for the next part where we make it all numerically accessible the Discretization.


Timetable:

00:00 Why we need a Macroscopic Perspective
01:44 Particles Collective Behavior
05:33 Using Equilibria for Reduction
08:17 Statistical Mechanics and Rarefied Gas Dynamics
12:00 Continuum Gas Dynamics
16:09 Building Macroscopic Quantities
23:05 Linking Macroscopic Quantities
34:09 Recap


Selected Papers and Learning Resources:

Sorted by Topics:
01:44 Local (Non)Equilibrium; Necessity of Collisions; Fluctuations; Molecular Chaos; Initial Perturbation; Statistical Perspective; Statistical Ensemble Averaging; Time Reversibility (to be discussed), Equilibria of different DegreesofFreedom (to be discussed): [1,2,3]
08:17 Rarefied Gas Dynamics: [1,4]
08:17 Phase Space (oneparticle vs. Nparticle): [1,5,6]
08:17 Boltzmann Equation derived via BBGKY Hierarchy from Liouville Theorem: [6]
12:00 Continuum Gas Dynamics, Continuum Hypothesis/Assumption, Alternative Flow Regimes Classifications: [1]
12:00 Local Knudsen Number and alternative Rarefaction Indicators: [1,4]
16:09 Macroscopic Quantities: Density, Flow Velocity, Pressure, Temperature [1]
23:05 Macroscopic Equations: Conservation Laws; Mass; Momentum; Energy [1]
27:20 NavierStokes Equations; Densities of Forces; Pressure Gradient; Viscosity: [1,7]
27:41 Time Derivatives along with flow; Lagrangian vs. Eulerian Formulation; Lagrangian vs. Eulerian Coordinate Systems: [8]
30:12 Velocity and Temperature Profiles for Couette Flow: [9]
32:45 Macroscopic Equations: Equations of State; Ideal Gas Law; Calorically Perfect Gas: [1]

Selected References:
[1] Lecture Notes: from "http://volkov.eng.ua.edu/ME591_491_NE..." to "NEGD06"
[2] Paper: Maes, Christian, and Karel Netočný. "Timereversal and entropy." Journal of statistical physics 110.1 (2003): 269310.
[3] Paper: "Parker, J. G. Rotational and vibrational relaxation in diatomic gases. The Physics of Fluids 2.4 (1959): 449462."
[4] Paper: Macrossan, M. N. "Scaling parameters for hypersonic flow: correlation of sphere drag data.", 2007.
[5] Lecture Notes: "Cerfon, Antoine. Mechanics (Classical and Quantum). https://www.math.nyu.edu/~cerfon/mech..."
[6] Lecture Notes: "Kenkre, V. M.. Statistical Mechanics. https://www.unm.edu/~aierides/505/" specifically ".../bbgky2.pdf" & ".../bbgky3.pdf"
[7] Book: Anderson, John D. "Governing equations of fluid dynamics." Computational fluid dynamics. Springer, Berlin, Heidelberg, 1992. 1551.
[8] Essay: Price, James F. "Lagrangian and eulerian representations of fluid flow: Kinematics and the equations of motion." MIT OpenCourseWare, 2006.
[9] Paper: Marques Jr, W., G. M. Kremer, and F. M. Sharipov. "Couette flow with slip and jump boundary conditions." Continuum Mechanics and Thermodynamics 12.6 (2000): 379386.


Disclaimer:

This series focuses specifically on the aspect of information reduction in dynamical systems. For the sake of clarity, I had to omit many interesting aspects of the topics addressed in the video. So, the video itself is a reduction. :)


Please note:

Watching this video with very low resolution produces the continua right away :), thanks to the video compression!


I hope you enjoyed this little braintruffle!

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Thank you for watching and I hope to see you next time!