This is the first part of a series on computational fluid dynamics in which we build a fluid simulator from scratch.

We highlight the microscopic perspective of quantum mechanics, molecular dynamics, and kinetic gas theory that underlies and justifies fluid simulation formulations in the first place.

The microscopic perspective forms the foundation of the next part where we focus on the macroscopic perspective with concepts such as pressure, viscosity, temperature and flow velocity as well as its evolution over time.

Calendar:
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00:00 – What we are building
02:06 – Guiding principle – Information reduction
04:03 – Measuring the little things
07:09 – Quantum mechanics and wave functions
1:45 p.m. – Reduction of model orders
4:48 p.m. – Molecular dynamics and classical mechanics
26h50 – Kinetic theory of gases
30:23 – Recap

Selected articles and learning resources:
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05:03 Experience:
Article: /"Stodolna, Aneta S., et al. Hydrogen atoms under magnification: direct observation of the nodal structure of severe states. Physical Review Letters 110.21 (2013): 213001./"

06:49 Tomography of atomic and molecular orbitals:
Article: /"Vozzi, Caterina, et al. Generalized molecular orbital tomography. Nature Physics 7.10 (2011): 822-826./"
Article: /"Itatani, Jiro, et al. Tomographic imaging of molecular orbitals. Nature 432.7019 (2004): 867-871./"

07:24 Matter waves, double slit experiment:
Article: /"Jönsson, Claus. Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten. Zeitschrift für Physik 161.4 (1961): 454-474./"
Article: /"Jönsson, Claus. Multi-slit electron diffraction. American Journal of Physics 42.1 (1974): 4-11./"

07:57 Overview of quantum mechanics, wave packets, standing waves, eigenstates:
E-book: /"Mathur, Samir D. https://www.asc.ohio-state.edu/mathur.16/quantummechanics27-11-17/navigation.html/"
E-Book: /"van Dommelen, Leon. Quantum mechanics for engineers. https://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/index.html (2004)/"

4:01 p.m. Reduction of orders for models, modes:
Course notes: from /"Farhat, Charbel. Model Reduction. https://web.stanford.edu/group/frg/course_work/CME345/CA-CME345-Ch1.pdf/" to /"CA-CME345-Ch9/ "

5:17 p.m. Classical mechanics, phase space:
Course notes: /"Cerfon, Antoine. Mechanics (classical and quantum). https://www.math.nyu.edu/~cerfon/mechanics.html/"

6:15 p.m. Molecular dynamics, Born-Oppenheimer approximation, potential energy surface and unquantized approximation of energy levels:
Lecture Notes: /"Allen, Michael P. Introduction to Molecular Dynamics Simulation. Computational Soft Matter: From Synthetic Polymers to Proteins 23.1 (2004): 1-28./"
Article: /"Parker, JG Rotational and vibrational relaxation in diatomic gases. The Physics of Fluids 2.4 (1959): 449-462./"
Article: /"Valentini, Paolo, et al. Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface. Fluid Physics 27.8 (2015): 086102./"
E-book chapter: /"van Dommelen, Leon. Quantum mechanics for engineers. 9.2 The Born-Oppenheimer approximation. https://web1.eng.famu.fsu.edu/~dommelen/quantum/style_a/bo. html (2004)/"

20:11 One-dimensional hydrogen atom approximation for the Coulomb potential as opposed to the "true/" one-dimensional Coulomb potential:
/"Loudon, Rodney. One-dimensional hydrogen atom. American journal of physics 27.9 (1959): 649-655./"
/"Loudon, Rodney. One-dimensional hydrogen atom. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472.2185 (2016): 20150534./"

27:06 Kinetic theory of gases, (variable) approximation of molecules by hard sphere:
Course notes: from /"http://volkov.eng.ua.edu/ME591_491_NEGD/2017-Spring-NEGD-01-ElemKineticTheory.pdf/" to /"NEGD-06/"

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

I hope you enjoyed this little brain truffle!

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