Computational High-Energy
Astrophysics Group of
Stephan Rosswog
Stockholm University









The Lagrangian hydrodynamics code


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:
  • high-order Wendland kernels, each particle uses 300 neighbour particles for calculating densities and gradients
  • accurate gradients via matrix-inversion techniques; the symmetries in the gradient expressions enable (like standard SPH-approaches) exact conservation
  • "dissipation only where needed":
    • slope-limited reconstruction (similar to Finite Volume techniques)
    • entropy-based steering of dissipation parameters; details can be found *here*


  1. 3D Sedov-Taylor explosion

    • a Sedov-Taylor explosion is a strong, initially point-like explosion into a low-density environment
    • the exact solution is known (black line, second plot)
    • it is a good numerical test, because many codes (particle- and grid-based) 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 Wendland-kernel + 300 neighbours

  3. Kelvin-Helmholtz instability

  4. click on the following picture to play the movie (left:density; right: dissipation parameter) Full length Quicktime (40Mb)
    • 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 "pseudo-2D" (= thin 3D-slice) 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 slope-limited 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 entropy-method, on the right; for comparison keep in mind that many "traditional SPH" methods use a constant dissipation parameter of ~1

  5. Rayleigh-Taylor instability

    • Rayleigh-Taylor instabilities are another standard hydrodynamics test
    • test is run in "pseudo-2D" (= thin 3D-slice) with the full 3D code
    • the MAGMA2 results agree very well in this test with other state-of-the-art codes

  7. Schulz-Rinne tests

    • Schulz-Rinne (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

  9. Tidal disruptions

  10. 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:

    • Tidal Disruption Events (TDEs) pose serious computational challenges:
      • the disrupted star is often "spagettified" and much larger than the orignal stars
      • often self-gravity is important for structure of the debris and for weak encounters often leads to the re-formation of a central core in the centre of the "spagetti", see panel 3 in the first TDE plot
      • the geometry of the double-disruption remnant, in particular its self-gravity, poses a major challenge for most hydrodynamics methods