Kelvin-Helmholtz instability - Discontinuous Galerkin hydrodynamics

2D Simulation of a Kelvin-Helmholtz instability with 4th order discontinuous Galerkin (DG) and adaptive mesh refinement. The simulation starts with 64^2 cells and is refined down to an effective resolution of 4096^2 cells. Shown is the surface density of the fluid. DG offers several advantages over traditional finite volume (FV) methods.It directly solves also for the higher-order moments of the solution, no reconstruction is needed, resulting in an inherent conservation of angular momentum and less advection and diffusion errors compared to a FV method. Furthermore, DG is a higher-order method with a small stencil and many local computations, which renders it highly suitable for high performance computing on massively parallel systems.
You may find the corresponding publication on arXiv: arxiv.org/abs/1...

[@professor.joao.r.andrade]

Thank you very much for sharing this stunning visualization! I will use this video to explain turbulence scales to my students. Your work is greatly appreciated

[@michaelpieters1844]

Fantastic work! Thanks for making the article public!

[@gaurav.bhutani]

Amazing! Love those fractals. What mesh resolution did you use? It's a structured mesh, right?

[@m31coding]

Hi Gaurav! It's a structured adaptive mesh with an initial resolution of 64^2 cells. During the simulation the mesh is refined where the hydrodynamic gradients are large, resulting in an effective resolution of 4096^2.

[@petterlarsson7257]

oh my god this is literally a fractal

[@dwightlumain8645]

That's what i'm thinking!

[@StojanBarbaric]

Hell yeah it is, nature is all about fractal behaviour

[@sca4723]

Not as that, fractal are between dimentions not in the linear, or in the plane nor the 3d space, something between them, thats because the sum and división fot their sides and nodes aren't integers

[@petterlarsson7257]

@@sca4723 no. you are incorrect.

[@pabilbadoespecial]

Yes, this is a feature of turbulence. It's called the Kolmogorov cascade where you will develop a power-law spectrum of modes. This is a lot of talking but it basically means that if you zoom in the image it should look vaguely the same, i.e. fractal :)

[@nausetjf1202]

Imagine turning this into an awesome wallpaper

[@StankyPickle1]

Beautiful work!

[@Actual_Genius_Intellectual]

This is amazing!

[@wjrasmussen666]

This is so amazing!

[@asnryu2829]

what a beautiful work :D

[@arpit1993]

Hey Kevin, Great work! I had struggled with KH myself for a while. :) How did you visualize this? The visualization is as awesome as the calculations themselves!

[@nicolobadodi3423]

Just a question, what type of mesh is this? How can a cell have more than one neighbor for each side?

[@rishivallem]

Looks beautiful. What was the initial pertubation applied on the system?

[@gabrielmximo]

Congrats! What software did you used?

[@hiZarki]

nice channel! subscribed

[@DenisJurin]

Great visualization! so detailed! Is it better compared to 2D AREPO simulation with similar resolution? and how much memory do you store per one AMR cell?

[@m31coding]

Hey Denis, good to hear from you! I haven't done comparisons with the moving mesh code, but it will depend on the problem at hand. In 2D the number of base functions is 1/2*p*(p+1), where p is the order of the scheme. Hence for fourth order DG there are 10 weights stored per conserved variable in every cell. The paper will be online on Tuesday :) See you soon hopefully!

[@Renaissance_Engineer]

What software did you use to render this?

[@m31coding]

Thank you for your question. I created the individual frames with Python (Matplotlib) and combined them with ffmpeg to a video.

[@RobotTheIndustrial]

What did you use for the visualization?

[@m31coding]

Hi, thank you for your question. The answer is I wrote my own Python scripts using numpy and matplotlib. After creating the single frames I combined them to a movie with avconv.

[@kerch00]

@@m31coding How many seconds(about) does it take to calculate one of these frames in Python?

[@karlschuster8853]

Could you give us a comparison about Discontinuous Galerien Method and a Multidomain Decomposition Chebyshev Method?

[@m31coding]

Hi Karl, unfortunately I haven't worked on the method you suggested. Best regards!

[@mkraposhin]

Just curious. Why does initially sharp interface become smooth? Do you approximate equations with viscosity or this is due to the numerical viscosity?

[@m31coding]

Thank you for your question! Yes, I believe this can be attributed to numerical viscosity. The Euler equations, which the code solves, do not account for viscosity.

[@mkraposhin]

@@m31coding Thank you. Do you have any idea how to decrease it?

[@X0LODN0]

Hi bro I have a question maybe you know how it can be realized in 3d software like blender and etc.

[@Warzak77]

looks like you are simulating jupiter

[@AvanaVana]

And that’s how Jupiters are made

[@xiaoweizhu995]

Beautiful!!! This colour, haha, are you from swden?

[@ZZXAAV]

Any tips on adaptive mesh refinement? I need to implement an adaptive mesh code and any references would be greatly appreciated.

[@m31coding]

Hi! The code paper of the RAMSES code is a great reference: arxiv.org/abs/astro-ph/0111367 best, Kevin

[@JezzaParker]

What is the Reynolds number here?

[@JulienPotier]

Hi, I am interested in using this simulation if you allow me and with due credits of course in a fulldome planetarium movie about chaos. Do you have a 4096x4096 video of it?

[@m31coding]

Hi Julien, thank you for your request! Unfortunately I only have a 1920x1080 version, feel free to use it. A fulldome movie about chaos sounds great, have fun! Best regards!

[@readmypfp]

or it could be black holes growing

[@arthsojitra53]

Hey Kevin ! Great Visualization ! Did you use any numerical library/software!!

[@m31coding]

Hi, thanks for your comment! I implemented DG into the Arepo Code from scratch. In the meantime, Arepo is publicly available, you may check it out. Best regards!

[@arthsojitra53]

@@m31coding Thanks for the info !

[@tnapeepeelu]

video starts *Ukrainian anthem starts playing but is soon cut off*

[@tarantula-k6o]

BOKEEE

[@readmypfp]

this is a tsunami thrower that works using a tsunami

[@gjoe3756]

It looks like fractals

[@АлександрСикфестов]

галеркин! 😃

[@yaoooy]

fractals

[@triocute09]

Wtf art

[@dimitrisgkofas7787]

extrim

[@user-qw9yf6zs9t]

ukraine

[@not_estains]

heehee ukraine flag

[@Serghey_83]

Меандр