## 1 Introduction  
High-speed trains have been competitively developed around the world since the first line was launched in Japan in 1964. The competition accelerated after the running speed of the French high-speed train TGV V150 exceeded 574.8 km/h. Many relevant studies have been carried out by worldwide manufacturers seeking to develop the fastest train, because it manifests technological superiority over others. However, as the running speed of high-speed trains increased, noise emissions also inevitably increased. Modern high-speed trains have two main distinctive noise sources: rolling noise caused by the interaction between wheels and rail, and aerodynamic noise caused by flow around the train [1]. According to related studies, the sound power due to rolling noise is known to increase in proportion with the third power of train speed \(V\). On the other hand, the sound power of aerodynamic noise increases with \(V^{6}\) and \(V^{8}\) for dipole and quadrupole sources, respectively [1]. Therefore, the relative contribution of aerodynamic noise becomes more important as the travel speed of the train increases. It has been reported that aerodynamic noise sources begin to contribute more to the overall noise levels as the travel speed of the train exceeds 300 km/h [2]. Recently, several studies [2; 3; 4; 5; 6] were carried out on the aerodynamic noise of high-speed trains. Various methods such as full-scale measurements, scaled-model tests in a wind tunnel, and numerical approaches were used, and the common results were that the first bogie, the first pantograph, and the first intercoach spacing were the aerodynamic sources contributing most to the radiated noise field. However, these studies used a simplified external body model or only a single part of a train, and focused only on externally radiated noise. The ultimate goal of this paper was to develop reliable, systematic numerical methods for the prediction of interior cabin noise of a high-speed train, which is one of the critical issues for the product developers. However, the fact that the interior cabin noise is directly caused only by the vibration of the cabin body structures made it more challenging to understand and model the relevant physical mechanism. The vibration of cabin body structure can be induced by external flow, including the acoustic field, as well as by the interaction between wheels and rail. The former and the latter can be called flow-borne and structure-borne vibrations, respectively. However, the external flow fluctuations consist of incompressible and compressible waves. The former is sometimes called hydrodynamic fluctuation or pseudo-sound, and the latter is called an acoustic wave. Again, compressible waves can be generated by the structural vibration and/or aerodynamic noise sources. This fact implies that the accurate flow field predictions including the aerodynamic noise sources and their corresponding acoustic waves are essential for the accurate prediction of interior cabin noise of a high-speed train, under the assumption that the aerodynamic noise is more dominant in the overall noise of a high-speed train. In the present study, as a first step for achieving the ultimate goal, the systematic numerical methodology presented was used to obtain separate incompressible and compressible surface pressure fields in the frequency-wavenumber and time-space domains. First, LES (large eddy simulation) techniques were employed to predict the flow field, including the acoustic field, around a high-speed train running in an open field. Second, pressure fluctuations on the train surface were decomposed into incompressible and compressible ones using wavenumber-frequency analysis. The separation is based on the physical fact that the wave speeds of incompressible and compressible pressure waves are different from each other. Finally, the separated incompressible and compressible surface pressure fields in the space-time domain were obtained from the inverse Fourier transform of the wavenumber-frequency spectrum.