REMIX SPH

REMIX is an SPH scheme designed to alleviate effects that typically suppress mixing and instability growth at density discontinuities in SPH simulations (Sandnes et al. 2025). REMIX addresses this problem by directly targeting sources of kernel smoothing error and discretisation error, resulting in a generalised, material-independent formulation that improves the treatment both of discontinuities within a single material, for example in an ideal gas, and of interfaces between dissimilar materials. The scheme combines:

  • An evolved density estimate to avoid the kernel smoothing error in the standard SPH integral density estimate;

  • Thermodynamically consistent, conservative equations of motion, with free functions chosen to limit zeroth-order error;

  • Linear-order reproducing kernels with grad-h terms and a vacuum interface treatment;

  • A “kernel normalising term” to avoid potential accumulation of error in the evolved density estimate, such that densities are ensured to remain representative of the distribution of particle masses in the simulation volume;

  • Advanced artificial viscosity and diffusion schemes with linear reconstruction of quantities to particle midpoints, and a set of novel improvements to effectively switch between treatments for shock-capturing under compression and noise-smoothing in shearing regions.

To configure with this scheme, use

./configure --with-hydro=remix --with-equation-of-state=planetary

This scheme allows multiple materials, meaning that different SPH particles can be assigned different equations of state (EoS). Every SPH particle then requires and carries the additional MaterialID flag from the initial conditions file. This flag indicates the particle’s material and which EoS it should use. Note that configuring with --with-equation-of-state=planetary is required for this scheme, although for simulations that use a single, ideal gas EoS, setting all MaterialIDs to 0 and including

EoS:
    planetary_use_idg_def:    1

in the parameter file are the only EoS-related additions needed compared with other non-Planetary hydro schemes. Note also that since densities are evolved in time, initial particle densities are required in initial conditions.

We additionally recommend configuring with --with-kernel=wendland-C2 and with

SPH:
  resolution_eta:        1.487

in the parameter file for improved hydrodynamic behaviour and since this is the configuration used for the validation simulations of Sandnes et al. (2025).

The current implementation of the REMIX hydro scheme has been validated for planetary applications and various hydrodynamic test cases, and does not include all necessary functionality for e.g. cosmological simulations.

Default parameters used in the artificial viscosity and diffusion schemes and the normalising term (see Sandnes et al. 2025) are:

#define const_remix_visc_alpha 1.5f
#define const_remix_visc_beta 3.f
#define const_remix_visc_epsilon 0.1f
#define const_remix_visc_a 2.0f / 3.0f
#define const_remix_visc_b 1.0f / 3.0f
#define const_remix_difn_a_u 0.05f
#define const_remix_difn_b_u 0.95f
#define const_remix_difn_a_rho 0.05f
#define const_remix_difn_b_rho 0.95f
#define const_remix_norm_alpha 1.0f
#define const_remix_slope_limiter_exp_denom 0.04f

These can be changed in src/hydro/REMIX/hydro_parameters.h.