Abstract Impeller stirred tanks are commonly used in the chemical processing industries (CPI) for a variety of mixing and blending technologies. Such processes require accurate modeling of the turbulent flow in the tank over a range of operating conditions (e.g. impeller speed), and in addition, require a computationally efficient solution strategy that can represent moving rigid geometric parts (impellers) in the tank. In the present study, a methodology is proposed that combines the advantages of the immersed boundary method (IBM) to represent moving rigid geometries with the efficiency of multi-block structured curvilinear meshes (to minimize wasted grid points) for the representation of overall complex domains. The IBM implementation on a multi-block curvilinear mesh is advocated for the simulations of impeller stirred tank reactors (STR) and has distinct advantages over other competing methods. In the present work, the curvilinear-IBM methodology is further combined with the curvilinear coordinate implementation of large eddy simulation (LES) technique to address the issue of modeling unsteady turbulent flows in the STR. To verify the implementation of IBM in a multi-block curvilinear geometry, a laminar STR with a stack of four pitched blade impellers on a single shaft is simulated and compared against experimental data. Verification of the combined IBM–LES implementation strategy in curvilinear coordinates is done through comparisons with the measurements of turbulent flow in a baffled STR with a single pitched blade impeller. For both laminar and turbulent STR, the predictions are in very good agreement with measurements. It is suggested here that this methodology can be reliably used as a predictive tool for the flow fields in STRs with complex geometries.