  We develop an unconditionally stable numerical method for solving the
coupling between two fluids (frictional forces/heatings, ionization, and
recombination), and investigate the dynamical condensation process of thermally
unstable gas that is provided by the shock waves in a weakly ionized and
magnetized interstellar medium by using two-dimensional two-fluid
magnetohydrodynamical simulations. If we neglect the effect of magnetic field,
it is known that condensation driven by thermal instability can generate high
density clouds whose physical condition corresponds to molecular clouds
(precursor of molecular clouds). In this paper, we study the effect of magnetic
field on the evolution of supersonic converging HI flows and focus on the case
in which the orientation of magnetic field to converging flows is orthogonal.
We show that the magnetic pressure gradient parallel to the flows prevents the
formation of high density and high column density clouds, but instead generates
fragmented, filamentary HI clouds. With this restricted geometry, magnetic
field drastically diminishes the opportunity of fast molecular cloud formation
directly from the warm neutral medium, in contrast to the case without magnetic
field.
