Abstract
In order to derive a simple one-dimensional approach that could handle fluid flows in smooth ducts as well as in ducts of discontinuous cross-section, we propose herein a Finite Volume approach that relies on an integral formulation of the multidimensional flow model. While focusing on Euler equations, we compare two-dimensional results with approximations obtained using the present approach, and also with the classical formulation for variable cross-sections using a well-balanced scheme. Numerical simulations confirm the ability of this integral method to provide approximations that compare well with 2D results. This method also enables to deal with all-even including vanishing-cross-section ducts. This approach may also be applied when considering other single-phase or multi-phase fluid flow models.
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Acknowledgments
Xavier Martin benefits from financial support through an EDF-CIFRE contract 2012/0838. This work has been achieved within the framework of the TITANS2 project. All computational facilities were provided by EDF. Authors also thank Thomas Pasutto for his help with Code_Saturne.
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Audebert, B., Hérard, JM., Martin, X., Touazi, O. (2014). A Simple Finite Volume Approach to Compute Flows in Variable Cross-Section Ducts. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_77
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DOI: https://doi.org/10.1007/978-3-319-05591-6_77
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