# A Separated-Flow Model for 2-D Viscous Flows around Bluff Bodies Using the Panel Method
###### Abstract
The proposed method is applied to the two-dimensional circular cylinder and the generic train and is mathematically and physically consistent with the real expected physics for the investigated problems. Based on inviscid incompressible potential flow theory, the panel method is applied to most general geometries by solving linear integral equations over the boundary. The main advantage of the method is to eliminate the need for a computational grid, owing to which it has been considered an appropriate design tool in many fields since the 1960s [20]. The panel method has a broad range of applications in industrial fields including trains. [PERSON] generalised the flow field around a train into four different regions according to the velocities induced by the cruising train: the nose region, the boundary-layer region, the near-wake region, and the far-wake region [21; 22]. In the nose region, the flow field for most of the trains is largely inviscid with low turbulence levels; that is, except for extremely blunt trains, where large-scale flow separation occurs. Similar results have been obtained using large eddy simulation (LES) by [PERSON] et al. [23]. [PERSON] [24] computed the potential flow around train heads with different geometries using a panel method and validated the results with model- and full-scale experiments. Based on the results, a simplified potential flow model, to compute the induced loads on track side objects for an axial symmetric head geometry and cylindrical track side objects, was developed [24]. By simplifying the moving train into a moving point, [PERSON] et al. [25; 26; 27; 28], [PERSON] and [PERSON] [29], and [PERSON] et al. [30; 31] investigated the train-induced effects on track-side infrastructures and head pressure waves using analytical methods. Although analytical models provide satisfactory solutions, they are only applicable after some major geometrical simplifications in the boundary conditions have been made. However, panel methods can be applied to more realistic geometries, and fulfil the boundary conditions on the actual surface [32]. [PERSON] et al. [33] and [PERSON] et al. [34] used boundary element methods(panel methods are the application of boundary element methods in fluid dynamics) and the three-dimensional panel method to solve the potential flow around the train nose. Due to the inviscid characteristics of the flow around the train head, potential flow solutions have been applied to predict the pressure variations due to the train passages. [PERSON] et al. [35] performed numerical simulations using the boundary element method to study the pressure changes caused by the train passage and validated the numerical model by comparing with the field test results. [PERSON] et al. [36] used the time-stepping low-order panel code, USAERO, based on the solutions of potential flow equations coupled with boundary layer and wake relaxation algorithms to simulate trains passing. The results, based on this method, agreed well with the experimental data in both trends and peak-to-peak pressure changes [36]. Some other researchers developed computing programs based on panel methods. For instance, [PERSON] et al. [37], [PERSON] [38], [PERSON] and [PERSON] [39], and [PERSON] et al. [40; 41] developed their own programs based on panel methods to predict the train-induced pressure loads and head pressure waves when trains pass each other. Their predicted results were tested by means of experiments or numerical simulations and showed good agreements [37; 38; 39; 40; 41]. [PERSON] [42] applied the inviscid three-dimensional source panel method to predict the pressure distributions in the cases of a single train at different yaw angles and a train passing a station or passing another train. The conventional panel method can only be applied to the potential flows such as the flow in the nose region. Additional models should be considered to simulate the separated-flow regions created by bluff bodies such as trains.