  The Santa Barbara cluster comparison project (Frenk et al. Frenk+1999)
revealed that there is a systematic difference between entropy profiles of
clusters of galaxies obtained by Eulerian mesh and Lagrangian smoothed particle
hydrodynamics (SPH) codes: Mesh codes gave a core with a constant entropy
whereas SPH codes did not. One possible reason for this difference is that mesh
codes are not Galilean invariant. Another possible reason is the problem of the
SPH method, which might give too much "protection" to cold clumps because of
the unphysical surface tension induced at contact discontinuities. In this
paper, we apply the density independent formulation of SPH (DISPH), which can
handle contact discontinuities accurately, to simulations of a cluster of
galaxies, and compare the results with those with the standard SPH. We obtained
the entropy core when we adopt DISPH. The size of the core is, however,
significantly smaller than those obtained with mesh simulations, and is
comparable to those obtained with quasi-Lagrangian schemes such as "moving
mesh" and "mesh free" schemes. We conclude that both the standard SPH without
artificial conductivity and Eulerian mesh codes have serious problems even such
an idealized simulation, while DISPH, SPH with artificial conductivity, and
quasi-Lagrangian schemes have sufficient capability to deal with it.
