Moving mesh domain adaptation technique - application to train induced wave propagation

Other conference contribution, 2005

Railways are an important part of the infrastructure in the society and the cost for their construction and maintenance is significant. Hence, understanding, predication and improvement of their performance is vital to utilize the resources in the best possible manner. Mathematical modeling and simulation of the railway mechanics provides a methodology to achieve this goal. In previous work, see e.g. [1]-[2], an integrated dynamic model of the entire 3D vehicle - track - underground system has been developed. The train has been modelled by rigid bodies, springs and dampers. The track and the underground have been modelled as elastic solids by FEM. This model has been successfully used to simulate and study the train induced wave propagation, see [1]-[2]. However, the size of the FE domain of the track and underground has been limited to approximately 200 m due to high computational cost (time). Hence, it has only been possible to follow the train running for about 200 metres. To be able to follow the train for many kilometres, something radical has to be done with the computational scheme. In this paper the following will be tested: 1. Moving mesh domain adaptation technique 2. Absorbing Boundary Layers The idea of the moving mesh is that the FE mesh should follow the moving train – or in other words, that in each time step only the domain in the vicinity of the train should be discretized by FEM. This scheme may be viewed as a special form of mesh adaptation where the mesh is located, graded and updated based on error estimation [3] or as a change to the governing equations by using a moving (convective) coordinate system [4]. In addition, the exterior infinite domain will be represented by an absorbing boundary layer (cf. [5] for a general introduction) rather than by the previously tested SBFEM to reduce computational time and complexity. The paper gives the full details of the computational scheme and numerical testing. REFERENCES [1] T. Ekevid and N.-E. Wiberg: Wave propagation related to high-speed train - a scaled boundary FE-approach for unbounded domains, Comput. Mehods Appl. Mech. Engrg., Vol. 191, pp. 3947–3964, (2002). [2] H. Lane, T. Ekevid and N.-E. Wiberg: Towards Integrated Vehicle-track-underground Modelling of Train Induced Wave Propagation. 4th European Congress on Computational Methods in Applied Sciences and Engineering. July 24-28 2004, Jyväskylä, Finland. [3] M. J. Baines, M. E. Hubbard and P. K. Jimack: Moving Mesh Finite Element Algorithm for the Adaptive Solution of Time-Dependent Partial Differential Equations with Moving Boundaries. Preprint submitted to Elsevier, 23 January 2005. [4] S. Krenk, L. Kellezi, S.R.K. Nielsen and P.H. Kirkegaard: Finite Elements and Transmitting Boundary Conditions for Moving Loads, EURODYN conference, June 7-10, 1999, Prague, Czech Republic. [5] I. Harari and Z. Shohet: On non-reflecting boundaries in unbounded elastic solids. Comput. Mehods Appl. Mech. Engrg., Vol. 163, pp. 123-139, (1998).