The collision of two white dwarfs is a quite frequent event in dense stellar
systems, like globular clusters and galactic nuclei. In this paper we present
the results of a set of simulations of the close encounters and collisions of
two white dwarfs. We use an up- to-date smoothed particle hydrodynamics code
that incorporates very detailed input physics and an improved treatment of the
artificial viscosity. Our simulations have been done using a large number of
particles (~ 4 \times 10^5) and covering a wide range of velocities and initial
distances of the colliding white dwarfs. We discuss in detail when the initial
eccentric binary white dwarf survives the closest approach, when a lateral
collision in which several mass transfer episodes occur is the outcome of the
newly formed binary system, and which range of input parameters leads to a
direct collision, in which only one mass transfer episode occurs. We also
discuss the characteristics of the final configuration and we assess the
possible observational signatures of the merger, such as the associated
gravitational waveforms and the fallback luminosities. We find that the overall
evolution of the system and the main characteristics of the final object agree
with those found in previous studies. We also find that the fallback
luminosities are close to 10^48 erg/s. Finally, we find as well that in the
case of lateral and direct collisions the gravitational waveforms are
characterized by large-amplitude peaks which are followed by a ring-down phase,
while in the case in which the binary white dwarf survives the closest
approach, the gravitational pattern shows a distinctive behavior, typical of
eccentric systems.Comment: 16 pages, 12 figures. Accepted for publication in MNRA