Скачать с ютуб Pressure Driven Pipe Flow Simulation in Python | Hagen-Poiseuille Profile в хорошем качестве

Pressure Driven Pipe Flow Simulation in Python | Hagen-Poiseuille Profile

Let's write Python/NumPy code for the simplest Navier-Stokes simulation in CFD, a pipe flow with periodic boundary conditions that is driven by a constant pressure gradient. Over time, the Hagen-Poiseuille parabolic profile will develop. Download the source-code here: https://github.com/Ceyron/machine-lea... Due to the viscous effects of the Navier-Stokes equations, the flow is creating boundary layers near solid wall boundary conditions. In this video, we look at a pipe flow for which the top end bottom edge of the domain is a wall Boundary Condition. This symmetry forces the initially uniform velocity profile to attain a parabolic shape. The pipe flow driven by a pressure gradient is also one of these rare cases for which we actually have an analytic solution to the Navier-Stokes equations, the law of Hagen Poiseuille. https://en.wikipedia.org/wiki/Hagen%E... Although we are using a time-stepping here, the actual trajectory is not really relevant, once we reach a stead state. You can think of the time-stepping here as a way to circumvent the nonlinearity in our equation through a couple of steps of explicit approximations. ------- 📺 : If you like my way of teaching and love fluid dynamics (that's of course a jackpot), take a look at this video:    • Pressure Driven Pipe Flow Simulation ...   📝 : 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-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler   and   / felix_m_koehler   💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim   ------- Timestamps: 00:00 Introduction 01:21 The scenario with periodic Boundary Conditions 02:31 Expected Outcome 03:42 Simplifications & Discretizations 05:44 Solution Strategy / Algorithm 07:24 Imports 07:43 Defining Constants 09:17 Boilerplate 09:32 Creating a Mesh 11:05 Periodic Central Differences 13:31 Periodic Five-Point Stencil for the Laplace Operator 14:56 Time-Loop Setup 15:11 Initial Condition 16:42 Convection 17:17 Diffusion 17:31 Velocity Update with explicit Euler 18:44 Enforce Wall Boundary Conditions 19:07 Advancing in time 19:29 Interactive Visualization Setup 21:22 First Run 21:58 Plotting in Dark-Mode - why not? 22:41 Visualizing velocity profile 23:44 Discussing the Hagen-Poiseuille profile 24:37 Playing with the parameters 25:42 Stability Considerations 27:27 Outro