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A solution to the problem of predicting the air¯ow over a train entering a tunnel is presented using parallel processing and a novel moving boundary condition scheme. The moving boundary condition approach avoids some of the topological problems of traditional approaches to this problem such as ALE techniques and contact surfaces. The method is demonstrated using both incompressible and compressible¯ow solvers based on the GLS ®nite element formulation. Flow solutions are compared with experiment for a simple geometry and the method is demonstrated on an actual train geometry. IntroductionMany¯uid¯ow problems are characterized by the unsteady¯ow over multiple bodies which are moving relative to one another. Examples are the problem of a train entering a tunnel shown in Fig. 1 and problems created by the passing of fan blades over ®xed fan components. These problems require a method to accommodate the changing shape of the¯uid volume. A common approach to this problem is the arbitrary Langrangian-Eulerian (ALE) method in which the¯uid mesh is deformed to accommodate the changing¯uid volume shape. The governing equations are then rewritten in the moving reference frame. Another approach is to introduce a sliding¯uid-uid contact surface to accommodate the changing topology. This solution strategy is more dif®cult to implement for parallel computation because the changing relationship between nodes in the contact surface may affect the desired domain decomposition. A third approach employs a costly automatic remeshing strategy. Our approach is similar to that used by some volume-ofuid methods in which the effect of the solid components is treated using a moving boundary condition on nodes within the¯uid domain.In the problem solved here, the tunnel and train are in essence two solid bodies moving relative to one another. Figure 2 shows a schematic of the moving boundary condition method. In this method, the reference frame and ®nite element mesh are ®xed with respect to the train and the``effect'' of the tunnel is moved through the mesh at the train speed. As the tunnel boundary passes through thē uid, the¯uid velocities within the solid volume of the tunnel are ®xed with respect to the train. In actuality, the interface between the solid and¯uid is not modeled within the mesh, but the effect of the solid on the¯uid is modeled. For incompressible¯ow and compressible¯ow without heat transfer, the moving boundary condition can easily be made to satisfy the velocity boundary condition at the solid boundary (of the tunnel) and satis®es the continuity equation and momentum equations. The resulting strategy has several advantages vis-a-vis other methods as discussed later in this paper. One advantage is the elimination of contact surfaces so that the domain decomposition needed for parallel processing is only done once. This facilitates a fast and ef®cient solution and may make implementation easier.The purpose of this study was to predict the pressures and forces on a high speed train entering a tunnel. To gain a better u...

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