The armature and rail sizes of electromagnetic rail launcher vary greatly, and the refined 3D finite element computation occupies a large amount of physical memory. In order to enhance the economy of dynamic computation, this paper proposes an adaptive hexahedral mesh method based on mesh expansion, compression, and translation. In addition, split nodes are used on both sides of the contact surface, and interface conditions and frictional heat sources are constrained through point penalty function method to solve non-ideal sliding electrical contact problems. Comparative calculations with the same type of software and the same model are carried out, and the results calculated in this paper are consistent with the relevant results of MEAP3D. This paper also compares the EMRL calculation results of adaptive mesh model and constant mesh model to verify the reliability of the method. In addition, the C-type EMRLs are compared and analyzed. The results show that due to the influence of velocity skin effect, the dynamic inductance gradient of the rail gradually increases over time and is greater than the static value. The maximum difference between the two is 5.65% of the dynamic inductance gradient. The steel shell generates eddy currents, causing a decrease in armature velocity of 4.7 m/s under the small caliber launcher. The maximum eddy current density waveform of the shell exhibits two peaks. In the frictionless heat, the temperature of the armature is underestimated, and under the action of frictional heat, the trailing edge of the armature is ablated and melted.