This is the new scheme that will be used in EAGLE-XL. This scheme includes:

  • Durier & Dalla Vecchia (2012) time-step limiter

  • Density-Energy SPH

  • Thermal diffusion following Price (2012)

  • A simplified version of the ‘Inviscid SPH’ artificial viscosity (Cullen & Dehnen 2010), with a Balsara switch

  • A diffusion limiter, used to prevent energy leakage out of EAGLE supernovae (Borrow+ 2020).

The simplified version of the ‘Inviscid SPH’ artificial viscosity calculates the time differential of the velocity divergence explicitly, using the value from the previous step. We also use the Balsara switch instead of the improved neighbour-based limiter from Cullen & Dehnen 2010, to avoid matrix calculations.

To configure with this scheme, use

./configure --with-hydro=sphenix --with-kernel=quintic-spline --disable-hand-vec

The diffusion limiter is implemented to ensure that the diffusion is turned off in very viscous flows and works as follows:

float new_diffusion_alpha = old_diffusion_alpha;

const float viscous_diffusion_limit =
  diffusion_alpha_max *
  (1.f - maximum_alpha_visc_over_ngb / viscosity_alpha_max);

new_diffusion_alpha = min(new_diffusion_alpha, viscous_diffusion_limit);

The parameters available for this scheme, and their defaults, are:

    viscosity_alpha: 0.1  # Initial value for the alpha viscosity
    viscosity_length: 0.25  # Viscosity decay length (in terms of sound-crossing time)
    # These are enforced each time-step
    viscosity_alpha_max: 2.0  # Maximal allowed value for the viscosity alpha
    viscosity_alpha_min: 0.0  # Minimal allowed value for the viscosity alpha

    diffusion_alpha: 0.0  # Initial value for the diffusion alpha
    diffusion_beta: 0.25  # Timescale to raise the diffusion coefficient over
                          # (decay is on the sound-crossing time)
    # These are enforced each time-step
    diffusion_alpha_max: 1.0
    diffusion_alpha_min: 0.0

There is also a compile-time parameter, viscosity_beta that we set to 3.0. During feedback events, the viscosity is set to the compile-time hydro_props_default_viscosity_alpha_feedback_reset = 2.0 and the diffusion is set to hydro_props_default_diffusion_alpha_feedback_reset = 0.0. These can be changed in src/hydro/SPHENIX/hydro_parameters.h.

Pressure Floor

The pressure floor is implemented for this scheme. The pressure floor is used in the sound-speed and hence the time-step will be lower in this case than if the pressure floor was not taken into account. The only other impact of the pressure floor is in the force loop, where the sub-grid floor pressure is used instead of the pressure calculated from the internal energy and density.