ADAPTIVE SMOOTH PARTICLE HYDRODYNAMICS AND PARTICLE-PARTICLE COUPLED CODES - ENERGY AND ENTROPY CONSERVATION

We present and test a general purpose code, called PPASPH, for evolvin g self-gravitating fluids in astrophysics, both with and without a col lisionless component. In PPASPH, hydrodynamical properties are compute d by using the SPH (smoothed particle hydrodynamics) method while, unl ike most previous implementations of SPH, gravitational forces are com puted by a PP (particle-particle) approach. Other important features o f this code are as follows: (1) PPASPH takes into account the contribu tions of all particles to the gravitational and hydrodynamical forces on any other particle. This results in a better energy conservation. ( 2) Smoothing lengths are updated by an iterative procedure that ensure s an exactly constant number of neighbors around each gas particle. (3 ) Cooling processes have been implemented in an integrated form that i ncludes a special treatment to avoid a nonphysical catastrophic coolin g phenomenon. Such a procedure ensures that cooling does not limit the time step. (4) Hydrodynamics equations optionally include the correct ion terms (hereafter (V) over bar h terms) appearing when h(t, r) is n ot constant. Our code has been implemented by using the data parallel programming model on the Connection Machine (CM), which allows for an efficient unification of the SPH and PP methods with costs per time st ep growing as similar to N. PPASPH has been applied to study the impor tance of adaptive smoothing correction terms on the entropy conservati on. We confirm Hernquist's interpretation of the entropy violation obs erved in previous SPH simulations as a result of having neglected thes e terms. An improvement on the entropy conservation is not found by me rely considering larger numbers of particles or different N-s choices. The correct continuum description is only obtained if the (V) over ba r h correction terms are included. Otherwise, the entropy conservation is always rather poor as compared to that found for the total energy.