1 Introduction

Smoothed particle hydrodynamics was first introduced by Lucy (1977) and by Gingold & Monaghan (1977), and nowadays it is the most convenient approach to simulate a variety of three dimensional astrophysical problems, involving compressible hydrodynamics, due to its Lagrangian nature and also its remarkably-low computational cost in comparison to other techniques that involves 3D-grids or finite elements. The technique combines some properties of the distribution theory with the Monte Carlo approach of estimating multiple integrals. Essentially, SPH reduces the hydrodynamic equations of motion to an N-body problem by using particles to transport local average (smoothed) fluid properties. A more extended review on SPH is given by Monaghan (1992) and Benz (1990).

The present SPH code has the main features of the TreeSPH class ([Hernquist & Katz 1989]; hereafter HK89). Initially, the code was designed to run on vector machines. Thus, the structure and methods for the octal-tree construction, and even for the tree traversals, are based on some works in literature, regarding vectorization of tree codes ([Barnes 1990]; [Hernquist 1990]; [Makino 1990]). The evolution of the fluid quantities are performed by means of a modified second order leapfrog, conveniently adapted to deal with multiple time scales: more energetic particles are time integrated along smaller time-steps, while less energetic particles are integrated along larger time-steps so that orbits are syncronized according to a binary hierarchy of time-steps.

The astrophysical application for the present code is performed by studying three special cases of collision of two identical molecular clouds. This application was motivated by the fact that collisions of interstellar clouds, or cloud fragments, occur in a variety of astrophysical situations, and there is evidence that they can trigger fragmentation and, consequently, star formation (e.g., [Bash 1979]; [Greaves & White 1991]; [Icke 1979]; [Koo et al. 1994]). Examples range from the dynamical support of giant molecular clouds in spiral arms (e.g., [Bash 1979]; [Elmegreen 1989], 1990, 1992), to clump-clump collisions inside a molecular cloud. The possible outcomes of cloud collisions, like coalescence, fragmentation, or star formation, depend on many parameters, e.g., relative velocity, impact parameter, details of the cooling mechanism, which in turn depends on metallicity etc. This way, modeling fragmentation by cloud collision requires more complex terms enclosing physical parameters in the fluid equations of motion.

Both thermal energy equation and molecular cooling have the same treatment proposed by Monaghan & Lattanzio (1991, hereafter ML91). Moreover, the Dalgarno & McCray (1972, hereafter DM72) model is adopted to cool down faster the initial phases of the supersonic shock. In addition, we take into account the heat mechanism by cosmic rays and by the production of H₂ on the surface of dust grains.

The inclusion of magnetic effects in collision experiment shall be presented as the second part of this work in the next paper.