###### Abstract
Benefitting from the progress in the theory of computational fluid dynamics (CFD), the time-marching throughflow method can automatically predict the choking conditions, and it has the shock-capturing feature. This method provides an efficient and robust analysis tool for the subsonic, transonic, and supersonic flow and has been becoming more and more popular in the modern turbomachinery design and analysis. The first time-marching throughflow method based on the Euler equations was presented by [PERSON] [16]. Then, systematic works were carried out by [PERSON] [21; 22; 23] and some key points were studied, including the modeling of inviscid blade force and blade blockage, and the analysis of the properties of shock waves. [PERSON] and [PERSON] [24; 25] have been dedicated to developing a time-marching throughflow analysis tool, which incorporates the effects of viscous loss, flow deviation, air bleeding and injection, and throat choking. [PERSON] [26] attempted to construct a turbomachinery analysis and design system (TADS) at Allison Engine Company by coupling the time-marching throughflow and blade-to-blade models, which is similar to [PERSON]'s work. Further developments led to the Navier-Stokes-based throughflow model and progress in modeling the effects of 3D loss in [PERSON] and [PERSON]'s work [27; 28]. The potentials of the time-marching throughflow method were also investigated in the design tasks of both the axial compressor and turbine based on the solution of the inverse problem [29; 30; 31] and its coupling with advanced optimization methods [32; 33; 34]. Detailed works about axial turbine simulation were performed by [PERSON] et al. [35], aiming to incorporate the real gas capabilities and 3D flow features into the time-marching throughflow models. [PERSON] et al. [36] raised a novel inviscid blade force model and proved its superiority in computing robustness compared to the widely used ordinary-differential-equation-based one. Although the aforementioned works have shown the considerable superiorities of the time-marching throughflow method compared to the classical ones, its applications are still limited within the scope of axial turbomachinery. To the author's best knowledge, the time marching throughflow analysis of the centrifugal compressor has not been implemented in the open literature. This may be attributed to the very strong adverse pressure gradient and complex viscous effects commonly existing inside the centrifugal compressor. The former can result in a very low Mach number flow and even backflow, which significantly increases the stiffness of the throughflow-governing equations; meanwhile, the latter negatively affects the accuracy of the performance prediction for the centrifugal compressor. In the present paper, a viscous time-marching throughflow method for the centrifugal compressor simulation is presented. The method has the capability to predict both the overall performance at off-design points and the corresponding meridional flow details. A normally averaged throughflow model, rather than the circumferentially averaged one, was elaborately selected, preserving the rigorous conservation of flow parameters in transonic flow analysis. To overcome the convergence problem occurring in the throughflow simulation of the centrifugal compressors with a high pressure ratio, characteristic boundary conditions (CBCs) based on [PERSON]'s iteration method were developed and can greatly improve the computation robustness. To simulate the viscous effects, complete loss correlations deduced from the open literature were adopted, accounting for both the internal losses and parasitic losses inside the centrifugal compressor. Owing to all the efforts above, throughflow solutions of different kinds of centrifugal compressors can be efficiently obtained using the time-marching method. This paper is organized as follows.