A powerful fluid model to study the role of gas dynamics in a glow discharge considered as an excitation medium for XeCl lasers is presented. This model was employed using a numerical code including four strongly coupled parts: electric circuit equations, electron Boltzmann equation, kinetic equations and conservation equations. The theoretical formalism presented here is based on the two-dimensional Euler equations describing the perfect compressible fluid. The numerical calculations have been carried out considering the single shot regime and neglecting the gas flow. The monotonic upstream centred scheme for conservation laws corrections has been used in order to estimate the exchange flow surrounding the control volume walls. We show that the crossing discharge induces a thermal energy density enhancement located principally in the cavity centre.