6 ms·

Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh

24 points by gone35 1y ago

HelloUsername 1y ago
(HN never fails to give me titles that I can use for my own random music projects :P)
jauntywundrkind 1y ago
> is based on a mov- ing unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved ar- bitrarily. The visual examples at the bottom feel very impressive. I haven't diced fully in, but it feels like there's points where they need to be, that represent the simulation well. Where-as the previous grids couldn't adapt to the problem. Neat to see!
ted_dunning 1y ago
This is really nice work that solves a lot of practical problems related to fixed gridding. I wonder if this could be applied to electromagnetic simulations. Common systems in that field have even more serious problems with gridding.
antognini 1y ago
Worth noting that this paper is from 2009. For anyone interested they released the code about a decade later: https://arepo-code.org/getting-started https://arepo-code.org/getting-started
- hbrav 1y ago
  > about a decade later Practically the blink of an eye to a cosmologist!
moktonar 1y ago
Do this in time and not only in space, using energy-momentum as the metric and you get Gravity and General Relativity. They are so close and yet they don’t seem to see it.
curt15 1y ago
Is classical HPC still alive and well in the current neural network craze?
- semi-extrinsic 1y ago
  Definitely. There are techniques that purport to replace traditional PDE solvers (FNOs, LNOs, all sorts of PINNs, ...), but I have yet to see something that can give reasonable predictions of even a second-year grad student level fluid dynamics problem without extensive fine-tuning on an extremely similar problem.

24 points by gone35 1y ago

(HN never fails to give me titles that I can use for my own random music projects :P)

> is based on a mov- ing unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. The mesh-generating points can in principle be moved ar- bitrarily. The visual examples at the bottom feel very impressive. I haven't diced fully in, but it feels like there's points where they need to be, that represent the simulation well. Where-as the previous grids couldn't adapt to the problem. Neat to see!

ted_dunning 1y ago

This is really nice work that solves a lot of practical problems related to fixed gridding. I wonder if this could be applied to electromagnetic simulations. Common systems in that field have even more serious problems with gridding.

antognini 1y ago

Worth noting that this paper is from 2009. For anyone interested they released the code about a decade later: https://arepo-code.org/getting-started https://arepo-code.org/getting-started

hbrav 1y ago
> about a decade later Practically the blink of an eye to a cosmologist!

moktonar 1y ago

Do this in time and not only in space, using energy-momentum as the metric and you get Gravity and General Relativity. They are so close and yet they don’t seem to see it.

curt15 1y ago

Is classical HPC still alive and well in the current neural network craze?

semi-extrinsic 1y ago
Definitely. There are techniques that purport to replace traditional PDE solvers (FNOs, LNOs, all sorts of PINNs, ...), but I have yet to see something that can give reasonable predictions of even a second-year grad student level fluid dynamics problem without extensive fine-tuning on an extremely similar problem.