  Longitudinal oscillations of solar filament have been investigated via
numerical simulations continuously, but mainly in one dimension (1D), where the
magnetic field line is treated as a rigid flux tube. Whereas those
one-dimensional simulations can roughly reproduce the observed oscillation
periods, implying that gravity is the main restoring force for filament
longitudinal oscillations, the decay time in one-dimensional simulations is
generally longer than in observations. In this paper, we perform a
two-dimensional (2D) non-adiabatic magnetohydrodynamic simulation of filament
longitudinal oscillations, and compare it with the 2D adiabatic case and 1D
adiabatic and non-adiabatic cases. It is found that, whereas both non-adiabatic
processes (radiation and heat conduction) can significantly reduce the decay
time, wave leakage is another important mechanism to dissipate the kinetic
energy of the oscillating filament when the magnetic field is weak so that
gravity is comparable to Lorentz force. In this case, our simulations indicate
that the pendulum model might lead to an error of ~100% in determining the
curvature radius of the dipped magnetic field using the longitudinal
oscillation period when the gravity to Lorentz force ratio is close to unity.
