## 1 Introduction
[11] conducted an iteration scheme to overcome the poor convergence problem of suction pressure. In all the above works the pipeline system were strongly approximated as simple pipe elements and plenum geometries together with additional correction to match experimental results. To model a detailed characterization of complex fluid domain, some authors took advantage of acoustic finite element method (FEM) for geometries with single input and single outlet [12] and geometries with multi-port [13]. However, the linear hybrid models are mainly limited in the event of acoustic resonant response or pressure pulsations with large amplitude [14], especially for variable-speed compression systems due to the impossible whole resonance avoidance. Numerical calculation of 1D unsteady gas-dynamics is much more appropriate in the analysis of pulsations. [PERSON] et al. [15] applied the Euler method to solve equations of first thermodynamic law and mass conservation for cylinder volume and the Method of Characteristics (MOC) to calculate the second-order hyperbolic non-linear partial differential equations. [PERSON] et al. [16] applied finite disturbance theory and four-pole method to predict pressure pulsations in a reciprocating compressor system and highlighted that the predictions of finite disturbance theory were much more accordance with experimental data than results from acoustic wave theory. [PERSON] and [PERSON] [17] developed a transient gas dynamic mathematical model for the simulation of compressor performance and pressure pulsations, which considered thermodynamics with gas leakage, kinematics, valve dynamics, gas flow through valves and transient unsteady flow in the duct system. [PERSON] et al. [18] revealed that pulsations can be damped by large piping volumes with weak impedances, and conversely amplified by strong impedance systems. In a general conclusion of these first studies, one can deduce that the hybrid model with in-pipe 1D gas dynamics results in great benefits respect to both the levels of accuracy and the computational cost. This up to date case is to model complex fluid domains. To summarize the aforesaid discussion, a question occurs: a variable-speed reciprocating compressor with multi-port complex plena is how to be modelled with a high level of trade-off between accuracy and computational cost. The previous literature survey demonstrates that few works have answered this question. This work aims to handle with this question through building in detail a new hybrid numerical model which, to the authors' best knowledge, represents a further step in the compressor modelling. This hybrid model extensively combines the lumped parameter approach, gas dynamics and acoustic FEM characterization. The modeling technique shares the advantages of the existing modelling method previously commented in the sense of mutual interaction between compressor and the pipelines, high level of details for complex fluid domains, large amplitudes of pressure pulsation and low computational cost. To this end, the hybrid model is implemented in commercially available software MATLAB and thermodynamic properties of the working fluid are obtained by calling the NIST REFPROP database [19]. A comparison analysis between this model and the hybrid model with gas dynamics is carried out, together with experimental data.