This work concerns the variational formulation and the numerical computation of internal acoustic problems with absorbing walls. The originality of the proposed approach, compared to other existing methods, is the introduction of the normal fluid displacement field on the damped walls. This additional variable allows to transpose formulations in frequency domain to time domain when the fluid is described by a scalar field (pressure or fluid displacement potential). With this new scalar unknown, various absorbing wall models can be introduced in the variational formulation. Moreover, the associated finite element matrix system in symmetric form can be solved in frequency and time domain.