LBM Fluid Simulation in Python with JAX | van Karman Vortex Street

Web Reference: Aug 25, 2015 · The following relationship is key to understand the link between lbm and lbf: 1 lbf=32.174 lbm ft/s^2 Arm yourself with this knowledge so that you can fight the good fight: the next time you hear someone say that pound-mass and pound-force are the same thing, you can confidently say they are not! Feb 16, 2021 · I have a question about work measured in foot-pound. Let's say we have a 10 pound-mass (10 10 lbm lb m) object. Then since that 10 pound-mass (10 10 lbm lb m) object gives 10 pound-force (10 10 lbf lb f) due to gravity, if we raise that object 2 feet, the work is 20 foot-pound (20 20 ft ⋅lbf ft lb f). I was wondering if I am right. Mar 1, 2024 · Example values for jet fuel include LHV equal to 18400 BTU/lbm (used with the default gas tables and does not include heat of formation) and enthlapy (used with Cantera generated gas tables and including heat of formation) equal to -1200 BTU/lbm. Note, negative numbers are okay, since the enthalpy is based on a reference zero value."

YouTube Excerpt: The Lattice-Boltzmann Method is an approach to fluid simulation that works on the Mesoscopic Scale of Fluid Motion. It is heavily influenced by statistical mechanics. Let's implement it in the JAX Deep Learning Framework. Here is the code: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/simulation_scripts/lattice_boltzmann_method_python_jax.py One of the best books on the Lattice Boltzmann Method: https://link.springer.com/book/10.1007/978-3-319-44649-3 ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-learning-and-simulation 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff: https://www.linkedin.com/in/felix-koehler and https://twitter.com/felix_m_koehler 💸 : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim ------- Timestamp: 00:00 Introduction 00:25 About LBM 00:52 van Kármán vortex street 01:41 LBM Discretization 02:11 The Algorithm 04:01 D2Q9 Grid 04:55 Data Array Shapes 05:21 Involved Computations 06:22 Flow Prescription 07:02 Imports 07:55 Defining Simulation Constants 09:59 Defining D2Q9 Grid Constants 17:22 Density Computing Function 18:05 Macroscopic Velocity Computing Function 21:15 Equilibrium Computing Function 25:20 Boilerplate 25:42 Enable Double Precision 26:05 Fluid Configuration 27:15 The Mesh 28:02 Obstacle Mask 29:51 Prescribed Velocity Profile 31:16 Algorithm as Update Function 31:45 (1) Prescribe Outflow BC 33:22 (2) Compute Macroscopic Quantities 34:09 (3) Prescribe Inflow BC 37:05 (4) Compute Discrete Equilibrium Velocities 37:40 (3) Prescribe Inflow BC (cont.) 38:19 (5) Collide according to BGK 39:16 (6) Bounce-Back BC 40:56 (7) Stream alongside Lattice Velocities 44:11 Initial Condition 45:14 Time Iteration 45:50 Visualization 52:28 Bug Fixing 54:00 Just-In-Time Compilation with JAX 55:03 Discussion of the Plot 57:16 Outro

The Lattice-Boltzmann Method is an approach to fluid simulation that works on the Mesoscopic Scale of Fluid Motion. It is heavily influenced by...

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