HYDRA - AN ADAPTIVE-MESH IMPLEMENTATION OF P(3)M-SPH

We present an implementation of smoothed particle hydrodynamics (SPH) in an adaptive particle-particle-particle-mesh (AP(3)M) algorithm. The code evolves a mixture of purely gravitational particles and gas part icles. SPH gas forces are calculated in the standard way from near nei ghbors. Gravitational forces are calculated using the mesh refinement scheme described by Couchman (1991). The AP(3)M method used in the cod e gives rise to highly accurate forces. The maximum pairwise force err or is set by an input parameter, For a maximum pairwise force error of 7.7%, the rms error in a distribution of particles is approximate to 0.3%. The refined-mesh approach significantly increases the efficiency with which the neighbor particles required for the SPH forces are loc ated. The code, ''Hydra,'' retains the principal desirable properties of previous P(3)M-SPH implementations; speed under light clustering, n aturally periodic boundary conditions, and easy control of the accurac y of the pairwise interparticle forces. Under heavy clustering the cyc le time of the new code is only 2-3 times slower than for a uniform pa rticle distribution, overcoming the principle disadvantage of previous implementations-a dramatic loss of efficiency as clustering develops. A 1000 step simulation with 65,536 particles (half dark, half gas) ru ns in one day on a Sun Sparc10 workstation. The choice of time integra tion scheme is investigated in detail. We find that a simple single-st ep predictor-corrector type integrator, which is equivalent to Leapfro g for velocity-independent forces, is the most efficient. A method for generating an initial distribution of particles by allowing a uniform temperature gas of SPH particles to relax within a periodic box is pr esented. The average SPH density that results varies by approximate to +/-1.3%, This is the fluctuation amplitude on roughly the Nyquist fre quency; for smaller wavenumbers the fluctuations have lower amplitudes . We present a modified form of the Layzer-Irvine equation which inclu des the thermal contribution of the gas together with radiative coolin g. The SPH and time integration schemes were tested and compared by ru nning a series of tests of sound waves and shocks. These tests were al so used to derive time-step constraints sufficient to ensure both ener gy and entropy conservation. We have compared the results of simulatio ns of spherical infall and collapse with varying numbers of particles, We show that many thousands of particles are necessary in a halo to c orrectly model the collapse. As a further test, the cluster simulation of Thomas & Couchman (1992) has been rerun with the new code, which i ncludes a number of improvements in the SPH implementation. We find cl ose agreement except in the core properties of the cluster which are s trongly affected by entropy scatter in the older simulation. This demo nstrates the crucial importance of conserving entropy in SPH simulatio ns.