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The Lagrangian hydrodynamics code
MAGMA2
Code paper: can be found *here*
In a nutshell:
MAGMA2 is a (mostly) Newtonian, completely Lagrangian hydrodynamics code. It is a
modern Smoothed Particle Hydrodynamics code ("Not your parents' SPH") that profits
from a number of novel elements:
 highorder Wendland kernels, each particle uses 300 neighbour particles for calculating densities and gradients
 accurate gradients via matrixinversion techniques; the symmetries in the gradient expressions enable (like standard SPHapproaches) exact conservation
 "dissipation only where needed":
 slopelimited reconstruction (similar to Finite Volume techniques)
 entropybased steering of dissipation parameters;
details can be found *here*
Examples:
3D SedovTaylor explosion
Comments:
 a SedovTaylor explosion is a strong, initially pointlike explosion into a lowdensity environment
 the exact solution is known (black line, second plot)
 it is a good numerical test, because many codes (particle and gridbased) produce
 (substantial) deviations from spherical symmetry
 a lot of noise behind the shock front
 the MAGMA2 solution shows no visible deviation from perfect symmetry
 in the second plot *every single particle* is shown (as red dots), i.e. we have an extremely well behaved particle distribution; this is the result of careful initial conditions and the Wendlandkernel + 300 neighbours
KelvinHelmholtz instability
click on the following picture to play the movie (left:density; right: dissipation parameter)
Comments:
 the shown Kelvin Helmholtz test is usually considered challenging for SPH and for "traditional formulations" the instability grows too slowly (if at all), see McNally et al. (2012)
 test is run in "pseudo2D" (= thin 3Dslice) with the full 3D code
 the MAGMA2 results show an accurate growth of the instability, even at low resolution, see Fig.19 in the MAGMA2 code paper
 the major difference compared with "standard SPH" comes from the slopelimited reconstruction, the second most import effect for this test comes from the more accurate gradients, see Fig. 20 in the code paper
 the movie shows the density on the left and the dissipation parameter, steered by our entropymethod, on the right; for comparison keep in mind that many "traditional SPH" methods use a constant dissipation parameter of ~1
RayleighTaylor instability
Comments:
 RayleighTaylor instabilities are another standard hydrodynamics test
 test is run in "pseudo2D" (= thin 3Dslice) with the full 3D code
 the MAGMA2 results agree very well in this test
with other stateoftheart codes
SchulzRinne tests
Comments:
 SchulzRinne (1993) designed a set of very challenging benchmark tests where complex wave patterns emerge and in particular a combination of shocks and vorticity creation occurs
 no analytic solutions are known for these tests, but many numerical solutions from modern Eulerian codes; actually these tests have hardly ever been tackled with SPH, it seems...
 again, the MAGMA2 results are in very good agreement with those from modern Eulerian codes
Tidal disruptions
partial disruption of 0.5 solar mass white dwarf by a 1000 solar mass black hole:
"double disruption" of a stellar binary by a supermassive black hole of 1 million solar masses:
Comments:
 Tidal Disruption Events (TDEs) pose serious computational challenges:
 the disrupted star is often "spagettified" and much larger than the orignal stars
 often selfgravity is important for structure of the debris and for weak encounters
often leads to the reformation of a central core in the centre of the "spagetti", see panel 3
in the first TDE plot
 the geometry of the doubledisruption remnant, in particular its selfgravity, poses a
major challenge for most hydrodynamics methods
