다운로드 "[Finite Element 6] Transient heat transfer (diffusion) in FEniCS: weak formulation & implementation"

After preparing the mesh to be imported into FEniCS in the previous video (https://www.youtube.com/watch?v=XnfvXn9bF4Y), we want to go for the actual simulation in this one. As we discussed before, FEniCS is a very powerful open-source finite element framework, similar to FreeFEM. In this video, we derive the weak formulation of the time-dependent heat/diffusion partial differential equation (PDE) and solve it on our helical shape mesh to obtain the temperature profile over time. Codes, models, and resources: In order to follow the videos and reproduce the output, you may want to use the ready codes and models instead of creating them from scratch using the instructions from previous videos. You can find all the relevant stuff, grouped for different episodes at http://tuxriders.com/videos/finite-element/ and https://github.com/TuxRiders/finite-element-intro You can see the rest of the episodes of the finite element series here: https://www.youtube.com/playlist?list=PL6fjYEpJFi7VgHQb-mr5giy2FQyf5y04L Applied numerical computing series, in which the underlying theories of these videos are discussed: https://www.youtube.com/playlist?list=PL6fjYEpJFi7UMDXtNiaF3eLlOKAM8Lrkf Topics covered: 🎯 Importing an external mesh into FEniCS 🎯 Deriving the weak form of the transient heat diffusion 🎯 Implementing the weak form in FEniCS models 🎯 Using GMSH to read the label of boundaries 🎯 Running FEniCS simulations in command-line 🎯 Visualizing the results in ParaView Lecturer: Mojtaba Barzegari https://mbarzegary.github.io/ To learn more about the goals of the TuxRiders project, please visit our website at http://tuxriders.com. Chapters in this video! ################ 00:00 - Intro 00:46 - Deriving the weak form of transient heat diffusion 04:19 - Writing the FEniCS code 16:11 - Checking mesh labels using GMSH 17:15 - Running the simulation and viewing the results