The purpose of this research is to help understand the influence of time-dependent fluid dynamics forces on the fatigue failure of turbomachinery blades. To that end, we conduct computational flow analysis of a turbocharger turbine with 13 rotor blades and 14 stator blades for precomputed time-dependent blade deformation patterns. The flow analysis is carried out for the rotor vibration modes corresponding to a set of natural frequencies lower than but close to the frequency associated with the upper end of the turbine operation range. The core computational method is the Space–Time Variational Multiscale (ST-VMS) method. The ST-VMS serves as a moving mesh method. That enables mesh-resolution control near the rotor surfaces and high-resolution boundary-layer representation. The core method is complemented with the “ST-SI-IGA,” which is the synthesis of the ST Slip Interface (ST-SI) method and ST Isogeometric Analysis (ST-IGA). The ST-SI enables the use of ST-VMS as a moving-mesh method even with the inner mesh rotating with the rotor. The ST-IGA with IGA basis functions in space brings superior accuracy to the geometry representation and flow solution. The ST-IGA with IGA basis functions in time enables higher-accuracy representation of the rotor motion and blade deformations.