Thanks for the kind comment 😊 This is VS code with the python extension and a dark theme. For this video, I didn't use a notebook, just a plain python file.
You're very welcome 🤗 I'm glad you enjoyed it. Generally speaking, validating numerical solvers is challenging. A first thing to check is if the two time steps in a trajectory (or the steady-state in a stationary simulation) fulfill the discretized PDE in that you plug the velocities into your discrete equations and computer a norm metric. If it is below a desired tolerance, it is a correct solution to the discrete problem. For the specific algorithm presented here that might not be too easily possible because we do not iterate Back and forth between momentum and continuity equation which would be necessary to ensure both are solved to the desired degree. Another approach would be to use test problems (like the lid-driven cavity) for which reference values are available (for the lid-driven cavity, one often uses the values due to Ghia et al.). I would recommend you to check out chapter 20&21 of book "automated solution of differential equations by the finite element method" by logg et al.
Hi, It seems fenics has undergone a large update, and I'm using the latest dolfinx to rewrite the code. However, there is seems a large gap. Do you have any example by using dolfinx? Thanks.
Yes, they made a bigger upgrade, also renewing some of the API. I haven't used it yet, unfortunately. The update of the FEniCs tutorial videos is on my to-do list but not of the highest priority atm. This tutorial is the first thing that popped up, maybe you find it helpful: jsdokken.com/dolfinx-tutorial/
Would be great if you did a variable density fluid, ie. Euler equation + viscosity coupled with advection of density. Everywhere density is constant, viscosity is constant, and fluid incompressible all the time. Doing something out of the mold would be very special.
That's a cool suggestion. I will note that down. :) I do not have much experience with compressible flows yet. From my engineering background, I would say that they mostly only relevant for high-speed aerodynamics (like fighter jets etc.). Almost all other engineering CFD is incompressible (or at least in the incompressible limit). Though, I can understand that it can become boring :D. Although, the saddle point structure of the incompressible NS is also very challenging, mathematically speaking.
@@MachineLearningSimulation yes I know. I'm a physics student an fluids are very difficult. But with the power of the computer, you can do that crazy stuff.
Thank you for the nice explanation. I still have problems understanding the solution strategy and derivation of the weak forms. Is it able for you to make a video like the ones for the heat equation and linear elasticity to explain in detail the solution strategy and weak form-derivation? I would also appreciate any suggestions from the literature to clarify the issue.
Hi, thanks for the comment 😊 Are you referring to the weak form? If so, then to my best knowledge FEniCS does not accept the strong form of the PDE. You always have to present your problem in weak form. Hence, FEniCS does not have a routine to translate the problem for you.
Unfortunately, I do not have much experience with periodic BCs in FEniCS, maybe you find this pointer to the FEniCS tutorials helpful: fenicsproject.org/olddocs/dolfin/1.4.0/python/demo/documented/periodic/python/documentation.html
I think it should be since all videos are in one Playlist: th-cam.com/play/PLISXH-iEM4Jl0-G1CpvG-mhrV0233tG_D.html But I will set a flag in the TH-cam settings such that those videos are best watched in order 😊
Thank you. This is super helpful as an intro to fenics for fluid.
Thanks a lot for the kind feedback 😊
Very Nice, can I know the software that you use in this video,please? I am using Jupyter notebook.
Thanks for the kind comment 😊
This is VS code with the python extension and a dark theme. For this video, I didn't use a notebook, just a plain python file.
Hey! Thank you so much for the video. Is there any way to validate that the solver indeed gives the velocities expected?
You're very welcome 🤗 I'm glad you enjoyed it.
Generally speaking, validating numerical solvers is challenging. A first thing to check is if the two time steps in a trajectory (or the steady-state in a stationary simulation) fulfill the discretized PDE in that you plug the velocities into your discrete equations and computer a norm metric. If it is below a desired tolerance, it is a correct solution to the discrete problem. For the specific algorithm presented here that might not be too easily possible because we do not iterate Back and forth between momentum and continuity equation which would be necessary to ensure both are solved to the desired degree.
Another approach would be to use test problems (like the lid-driven cavity) for which reference values are available (for the lid-driven cavity, one often uses the values due to Ghia et al.).
I would recommend you to check out chapter 20&21 of book "automated solution of differential equations by the finite element method" by logg et al.
Hi,
It seems fenics has undergone a large update, and I'm using the latest dolfinx to rewrite the code. However, there is seems a large gap. Do you have any example by using dolfinx?
Thanks.
Yes, they made a bigger upgrade, also renewing some of the API. I haven't used it yet, unfortunately. The update of the FEniCs tutorial videos is on my to-do list but not of the highest priority atm.
This tutorial is the first thing that popped up, maybe you find it helpful: jsdokken.com/dolfinx-tutorial/
Would be great if you did a variable density fluid, ie. Euler equation + viscosity coupled with advection of density. Everywhere density is constant, viscosity is constant, and fluid incompressible all the time. Doing something out of the mold would be very special.
That's a cool suggestion. I will note that down. :)
I do not have much experience with compressible flows yet. From my engineering background, I would say that they mostly only relevant for high-speed aerodynamics (like fighter jets etc.). Almost all other engineering CFD is incompressible (or at least in the incompressible limit). Though, I can understand that it can become boring :D. Although, the saddle point structure of the incompressible NS is also very challenging, mathematically speaking.
@@MachineLearningSimulation yes I know. I'm a physics student an fluids are very difficult. But with the power of the computer, you can do that crazy stuff.
Please make more FEniCS videos
More to come in the next weeks ;)
Thank you for the nice explanation. I still have problems understanding the solution strategy and derivation of the weak forms. Is it able for you to make a video like the ones for the heat equation and linear elasticity to explain in detail the solution strategy and weak form-derivation?
I would also appreciate any suggestions from the literature to clarify the issue.
Thanks a lot for the kind words. :)
This explanation for the NS equations together with Chorin's projection will be released tomorrow ;)
is there any way we that get the variational form by using fenics ?
Hi, thanks for the comment 😊
Are you referring to the weak form? If so, then to my best knowledge FEniCS does not accept the strong form of the PDE. You always have to present your problem in weak form. Hence, FEniCS does not have a routine to translate the problem for you.
Any comment on how to implement periodic boundary conditions on for example at the left and right wall? I'm having problems with PBCs in fenics
Unfortunately, I do not have much experience with periodic BCs in FEniCS, maybe you find this pointer to the FEniCS tutorials helpful:
fenicsproject.org/olddocs/dolfin/1.4.0/python/demo/documented/periodic/python/documentation.html
Wonderful
Thank you! Cheers!
Hallo, was ist denn bitte der Editor? LG
Hi,
das ist Visual Studio Code mit der Python Extension. Für das Video habe ich mit OBS aber nur einen Teilbereich des Bildschirms aufgenommen.
Visual Studio Code
when you post new video , kindly must use fenics word with it
Hi, thanks for the comment. 😊
What do you mean by this? There is FEniCS in the title of the video? Or do you mean a post on social media
@@MachineLearningSimulation start with fenics tutorial , just like this video
I think it should be since all videos are in one Playlist: th-cam.com/play/PLISXH-iEM4Jl0-G1CpvG-mhrV0233tG_D.html
But I will set a flag in the TH-cam settings such that those videos are best watched in order 😊
@@MachineLearningSimulation Thank you
You're welcome 😊