Adaptive Smooth Particle Hydrodynamics and Particle-Particle Coupled Codes: Energy and Entropy Conservation

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We present and test a general purpose code, called PPASPR, for evolving self-gravitating fluids in astrophysics, both with and without a collisionless component. In PPASPH, hydrodynamical properties are computed by using the SPH (smoothed particle hydrodynamics) method while, unlike most previous implementations of SPH, gravitational forces are computed by a PP (particle-particle) approach. Other important features of this code are as follows: (1) PPASPR takes into account the contributions 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 ensures an exactly constant number of neighbors around each gas particle. (3) Cooling processes have been implemented in an integrated form that includes a special treatment to avoid a nonphysical catastrophic cooling phenomenon. Such a procedure ensures that cooling does not limit the time step. (4) Hydrodynamics equations optionally include the correction terms (hereafter ∇h terms) appearing when h(t, r) is not constant. <P />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 step growing as ∼N. <P />PPASPR has been applied to study the importance of adaptive smoothing correction terms on the entropy conservation. We confirm Hernquist's interpretation of the entropy violation observed in previous SPR simulations as a result of having neglected these terms. An improvement on the entropy conservation is not found by merely considering larger numbers of particles or different N<SUB>s</SUB> choices. The correct continuum description is only obtained if the ∇h correction terms are included. Otherwise, the entropy conservation is always rather poor as compared to that found for the total energy.