Description of the flow equations around a high speed train inside a tunnel

The present article focuses on the analysis of the equations that describe the flow when a high speed train enters a tunnel. The disparity in time and length scales allows the problem to be decomposed in different regions and regimes when matched appropriately produce the full description of the flow. The aforementioned regions are the flow upstream and downstream of the train, the areas near the nose and tail of the train, and the flow in the gap between the train and the tunnel. The regimes are analysed based on the flow regions, time scales, length scales and velocity scales. All those regions and regimes are conveniently formulated and the flow key scales are analysed and described, which allows for a simplified and robust formulation. The aforementioned formulation is implemented in a computational program that needs some external coefficients, namely the pressure signature of the train, that should be obtained only once and it could be derived from experimental data or CFD. Comparison with experimental and numerical data from other references are provided. Finally, the thermal problem is briefly introduced and some comments on the tunnel cooling problem are considered.