High-fidelity simulations of multi-phase flows represent a crucially relevant tool in the design process of many different field of engineering. The sudden change of density, viscosity and thermodynamic properties at the interface between two immiscible fluids poses a great challenge in terms of numerical modelisation. The development of reliable, accurate and robust discretisation techniques to deal with this type of problems consequently represents an unavoidable step to uncap the simulation of challenging scenarios as the ones commonly encountered in the aeronautical industry. In the present work the spectral difference scheme is employed in the discretisation of the five equation model equipped with the additional Allen-Cahn regularisation terms for interface capturing purposes [1, 2]. Within the framework of the spectral difference scheme, in order to mitigate pressure oscillations in proximity of material interfaces in two-phase flows, a change of variables (from conservative to primitive) in the extrapolation to the flux points step is used in order to alleviate the non-linearity of the stiffened-gas equation of state. A series of numerical tests of increasing complexity are considered in order to assess the robustness of the solver, including both kinematic and two-phase test cases. From the former group, the Rider-Kothe vortex is studied in order to quantify convergence properties of the scheme and mass conservation errors. Regarding two-phase flows, a series of more complex problems are considered: the Rayleigh-Taylor instability, a shock- droplet interaction and a three-dimensional, two-phase version of the Taylor-Green Vortex problem. Overall, the proposed approach shows good robustness in dealing with a large variety of classical test cases in the two-phase simulations community, advocating the advantages of using high-order discretisations. REFERENCES [1] P. Chiu, and Y. Liu, A conservative phase field method for solving incompressible two-phase flows. Journal of Computational Physics, Vol. 230, pp. 185-204, 2011. [2] S. Jain, A. Mani, P. Moin, A conservative diffuse-interface method for compressible two-phase flows. Journal of Computational Physics, Vol. 418, pp.109606, 2020.