A computer implemented method for the prediction of the performances of a compressor comprising at least a blade stage and at least a vanes stage, the method comprising the steps of: - modelling a Computational Fluid Dynamics CFD gas path including: - a compressor inlet passage comprising an upstream boundary where atmospheric pressure and temperature conditions are imposed, - at least a vane flow portion, at least a blade flow portion adjacent to the vane flow portion and at least a mixing plane, between the vane flow portion and the blade flow portion, and - a compressor outlet passage, - modelling the vanes and blades as non-adiabatic solids, - building a model of the rotor including at least a first rotor solid domain facing a plurality of vanes non-adiabatic solids and at least a second plurality of rotor solid domains attached to a plurality of blades non-adiabatic solids, the first and second rotor solid domains being adjacent to each other and modelled as non-adiabatic, - building a model of the stator including at least a first casing solid domain attached to a plurality of vanes non-adiabatic solids and at least a second casing solid domain facing a plurality of blades non-adiabatic solids, the first and second casing solid domains being adjacent to each other and modelled as non-adiabatic, - modelling a plurality of fluid to solid interfaces, each fluid to solid rotor interface providing an heat exchange link between a respective blade flow portion or vane flow portion and a radially adjacent rotor solid domain or casing solid domain, - modelling one or more solid rotor interfaces, each solid rotor interface providing a heat exchange link between a respective pair of adjacent rotor solid domains, and - modelling one or more solid stator interfaces, each solid rotor interface providing a heat exchange link between a respective pair of adjacent stator solid domains, - wherein the method further comprises the step of building a stationary fluid model of the air surrounding the casing, the stationary fluid model having a first inner boundary in contact with the casing solid domains and a second external boundary, opposite to the first boundary where atmospheric pressure and temperature conditions are imposed, and- wherein the stationary fluid model of the air surrounding the casing comprises a plurality of fluid domains, each being in contact with a respective casing solid domain, one or more fluid interfaces being modelled, each fluid interface providing a heat exchange link between a respective pair of adjacent fluid domains. - modelling a Computational Fluid Dynamics CFD gas path including: - a compressor inlet passage comprising an upstream boundary where atmospheric pressure and temperature conditions are imposed, - at least a vane flow portion, at least a blade flow portion adjacent to the vane flow portion and at least a mixing plane, between the vane flow portion and the blade flow portion, and - a compressor outlet passage, - a compressor inlet passage comprising an upstream boundary where atmospheric pressure and temperature conditions are imposed, - at least a vane flow portion, at least a blade flow portion adjacent to the vane flow portion and at least a mixing plane, between the vane flow portion and the blade flow portion, and - a compressor outlet passage, - modelling the vanes and blades as non-adiabatic solids, - building a model of the rotor including at least a first rotor solid domain facing a plurality of vanes non-adiabatic solids and at least a second plurality of rotor solid domains attached to a plurality of blades non-adiabatic solids, the first and second rotor solid domains being adjacent to each other and modelled as non-adiabatic, - building a model of the stator including at least a first casing solid domain attached to a plurality of vanes non-adiabatic solids and at least a second casing solid domain facing a plurality of blades non-adiabatic solids, the first and second casing solid domains being adjacent to each other and modelled as non-adiabatic, - modelling a plurality of fluid to solid interfaces, each fluid to solid rotor interface providing an heat exchange link between a respective blade flow portion or vane flow portion and a radially adjacent rotor solid domain or casing solid domain, - modelling one or more solid rotor interfaces, each solid rotor interface providing a heat exchange link between a respective pair of adjacent rotor solid domains, and - modelling one or more solid stator interfaces, each solid rotor interface providing a heat exchange link between a respective pair of adjacent stator solid domains, - wherein the method further comprises the step of building a stationary fluid model of the air surrounding the casing, the stationary fluid model having a first inner boundary in contact with the casing solid domains and a second external boundary, opposite to the first boundary where atmospheric pressure and temperature conditions are imposed, and- wherein the stationary fluid model of the air surrounding the casing comprises a plurality of fluid domains, each being in contact with a respective casing solid domain, one or more fluid interfaces being modelled, each fluid interface providing a heat exchange link between a respective pair of adjacent fluid domains.