AREPO – V. Springel. arXiv:0901.4107. Adaptive, moving, unstructured hydrodynamics, locally adaptive time-steps, self-gravity + Galilean Invariance i.e. Everything you ever wanted except MHD ;) 66 journal pages!. AREPO – V. Springel. Why do we want/need all these features?
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Adaptive, moving, unstructured hydrodynamics, locally adaptive time-steps, self-gravity + Galilean Invariance
i.e. Everything you ever wanted except MHD ;)
66 journal pages!
Circumcircle does not enclose
any other vertices.
Form usual state vector, flux function & Euler (conservation) equations
Fluid state described by cell averages
Use Euler equations + convert volume integral to surface integrals
w cell boundary velocity, w=0 for Eulerian code
Moving grids won’t follow flow perfectly so still need to include w term
Using Aij to describe orientation of faces
Unsplit – all fluxes computed in one step
Green-Gauss theorem over faces is inaccurate
Use a more complex construction
Where cij is vector to the centre of mass of face
e.g. construct density at a point by
Maintains second order accuracy in smooth regions
Apply slope limiter as well
It’s 1:07 am...
Simplest approach is to simply follow fluid speed of cell
Can lead to poor cell aspect ratios
Original distribution of cells
After 50 iterations of Lloyd’s algorithm
Treats cells as top-hat spheres of constant density
Force softening is applied but not actually necessary on the grids (cells maintain very regular spacing)
Carefully applied a correction force arising from different force softenings associated with each cell
1-d acoustic wave evolution
Interacting blast waves
Point explosion (i.e. Sedov-like test)
Gresho vortex problem
Noh shock test
Moving grid seems to handle contact discontinuity slightly better
No surprises here
IGNORE the red line on the plots ppt screwed up
At simulation time t=2.0
At simulation time t=2.0 – more mixing in the fixed mesh!
Solution becomes dominated by advection errors
Moving mesh solution is said to be “identical” regardless of v
Evrard collapse test (spherical collapse of self-gravitating sphere)
Zel’dovich pancake (1-d collapse of a single wave but followed in 2-d)
The “Santa Barbara” cluster (cosmological volume simulated with adiabatic physics)
“Trivial” problem of collapsing sphere of gas
Accretion shock is generated
Common test for self-grav hydro codes
Dark matter calculations very
close – thank goodness
Some significant differences
(residual would have been nice)
Appear closer than temps
Entropy profile hints at a core
For 1283 run
I can’t find any!
One suspects that the method might be somewhat slow at the moment
Probably not a bad thing right now – most of the computations are linear algebra on small matrices
Can decompose the problem well enough to keep parallel computers very busy...