Centrifugal compressors used in applications like enhanced oil recovery using gas re-injection and Carbon capture and sequestration operate at very high pressures and often have to to deal with supercritical CO2 which is considerably viscous. Increased viscosity leads to energy dissipation and introduces damping in the acousto-elastic interaction between supercritical CO2 and the impeller of a centrifugal compressor, thereby altering the frequency response of the system especially near resonant frequencies. In this paper, the damping introduced by viscothermal effects in such acousto-elastic systems is accounted for in a numerically efficient manner. The acoustics in the fluid are modelled using the Boundary Layer Impedance(BLI) model and the centrifugal impeller as a linear elastic structure. The coupled acousto-elastic system is then solved using the finite element method. The finite element solution becomes computationally expensive especially when working with large three-dimensional models. In order to reduce the computational cost, a model order reduction technique based on a multi-point second-order Arnoldi(SOAR) procedure is developed. It is demonstrated that the reduced order model significantly brings down the computational time while being sufficiently accurate. © Copyright 2015 by ASME.