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.
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