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On Robust and Adaptive Finite Volume Methods for Steady Euler Equations

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Theory, Numerics and Applications of Hyperbolic Problems II (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 237))

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Abstract

In this paper, a robust and adaptive framework of finite volume solutions for steady Euler equations is introduced. On a given mesh, the numerical solutions evolve following the standard Godunov process and the algorithm consists of a Newton method for the linearization of the governing equations and a geometrical multigrid method for solving the derived linear system. To improve the simulations, an h-adaptive method is proposed for more efficient discretization by means of local refinement and coarsening of the mesh grids. Several numerical issues such as the regularization of the system, selection of the reconstruction patch, treatment of the curved boundary, as well as the design of the error indicator will be discussed in detail. The effectiveness of the proposed method is successfully examined on a variety of benchmark tests, and it is found that all simulations can be implemented well with one set of parameters, which shows the robustness of the method.

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Acknowledgements

The research of Guanghui Hu was partially supported by 050/2014/A1 from FDCT of the Macao S. A. R., MYRG2014-00109-FST and MRG/016/HGH/2013/FST from University of Macau and National Natural Science Foundation of China (Grant No. 11401608). The research of Tao Tang was partially supported by the Special Project on High-Performance Computing of the National Key R&D Program under No. 2016YFB0200604, the National Natural Science Foundation of China under No. 11731006, and the Science Challenge Project under No. TZ2018001.

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Authors and Affiliations

  1. UM Zhuhai Research Institute, Zhuhai, Guangdong Province, China

    Guanghui Hu

  2. University of Macau, Macao S.A.R., Macau, China

    Guanghui Hu & Xucheng Meng

  3. Southern University of Science and Technology, Shenzhen, Guangdong Province, China

    Tao Tang

Authors
  1. Guanghui Hu
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  2. Xucheng Meng
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  3. Tao Tang
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Correspondence to Tao Tang .

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Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Hu, G., Meng, X., Tang, T. (2018). On Robust and Adaptive Finite Volume Methods for Steady Euler Equations. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-91548-7_2

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