Some Experiments with SPH

Smoothed Particle Hydrodynamics (SPH) is an attractive way to model hydrodynamical systems using techniques similar to standard N-body methods. In the large-N limit, SPH should reproduce solutions of the standard hydrodynamical equations. Early results with a new adaptive SPH code indicate that

• Increasing N_s, the number of particles per smoothing volume, does not always improve the sampling of the fluid variables. For N_s ~ 100 or more, clustering develops on scales of ~0.1 h, where h is the local smoothing length. This is probably a collective effect, since the pressure force between any two particles is always repulsive. Clustering can be suppressed by giving the smoothing function a non-zero slope at small separations.

• Adaptive SPH formulations usually neglect terms involving gradients of the smoothing length h; as shown by Hernquist (1993), this can cause significant errors in energy or entropy. The effect of these `grad-h' terms can be reduced by increasing both N and N_s, but this brute-force solution appears far less efficient than the Hamiltonian approach of Nelson & Papaloizou (1994).

• The thermodynamic state of the fluid may be represented by either the internal energy u or the entropy function a(S). Both representations have advantages, but a(S) seems more convenient since (1) it is conserved in adiabatic flows, reducing the demands on the numerical integrator, and (2) failure of energy conservation then indicates the effect of neglecting grad-h terms.

Note: for images and animations of some SPH experiments, see this link.

Last modified: February 21, 1999