# ANARCHY-PU SPH¶

This scheme is similar to the one used in the EAGLE code. This scheme includes:

- Durier & Dalla Vecchia (2012) time-step limiter
- Pressure-Energy SPH
- Thermal diffusion following Price (2012)
- A simplified version of the ‘Inviscid SPH’ artificial viscosity (Cullen & Denhen 2010), with a Balsara switch.

More information will be made available in a forthcoming publication.

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=anarchy-pu --with-kernel=quintic-spline --disable-hand-vec
```

The scheme as-implemented in SWIFT is slightly different to the one implemented in the original EAGLE code:

- Pressure-Energy SPH is used instead of Pressure-Entropy SPH
- Artificial viscosity coefficients have changed – from minimal value of 0.1 to 0.0, and from length of 0.1 to 0.25. This is based on performance of hydrodynamics tests in SWIFT and may be to do with our choice of smoothing length definition.
- Recommended kernel changed from Wendland-C2 (with 100 Ngb) to Quintic Spline (with ~82 Ngb).

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

```
SPH:
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: 0.01 # 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/AnarchyPU/hydro_parameters.h`

.

# ANARCHY-DU SPH¶

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 in prep).

More information will be made available in a forthcoming publication.

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.

The diffusion limiter is implemented to ensure that the diffusion is turned ff 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:

```
SPH:
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/AnarchyPU/hydro_parameters.h`

.