[en] The functioning of a Vuilleumier heat pump with four variable-volume chambers and six heat exchangers was numerically simulated using a theoretical adiabatic physico-mathematical model. All four variable-volume chambers were assumed as adiabatic and the heat exchangers were considered as isothermal. The model uses the piston movement laws given by the mechanism and not simplified sinusoidal ones. The adiabatic functioning was described through thermodynamic diagrams showing pressure and temperatures cyclical variations inside the machine and inside each adiabatic chamber. The model allows to estimate the heat pump performances, highlighting the energy exchanged by the working agent inside heaters and coolers and the coefficient of performance. The adiabatic model is able to emphasize the energy transfer that appears between the branches of the machine, feature that simpler theoretical models do not have. This analysis of the functioning with the adiabatic model could be extended for a Vuilleumier heat pump that rejects heat at two different temperatures. (paper)