Applications of multi-dimensional schemes on unstructured grids for high-accuracy heat flux prediction

  • Yunbo Wan
  • Nianhua Wang
  • Laiping ZhangEmail author
  • Yewei Gui
Research Paper


The simulation of hypersonic flows with fully unstructured (tetrahedral) grids has severe problems with respect to the prediction of stagnation region heating, due to the random face orientation without alignment to the bow shock. To improve the accuracy of aero-heating predictions, three multi-dimensional approaches on unstructured grids are coupled in our Reynolds-averaged Navier–Stokes (RANS) solver, including multi-dimensional upwind flux reconstruction (MUP), multi-dimensional limiter (MLP-u2) and multi-dimensional gradient reconstruction (MLR). The coupled multi-dimensional RANS solver is validated by several typical verification and validation (V&V) cases, including hypersonic flows over a cylinder, a blunt biconic, and a double-ellipsoid, with commonly used prism/tetrahedral hybrid grids. Finally, the coupled multi-dimensional solver is applied to simulating the heat flux distribution over a 3D engineering configuration, i.e. a Hermes-like space shuttle model. The obtained numerical results are compared with experimental data. The predicted results demonstrate that the coupled multi-dimensional approach has a good prediction capability on aerodynamic heating over a wide range of complex engineering configurations.


Heat-flux prediction Unstructured grid Multi-dimensional gradient reconstruction Multi-dimensional limiter Multi-dimensional upwind scheme 



This work was supported partially by the National Key Research & Development Program of China (2016YFB020071) and the National Natural Science Foundation of China (Grants 11532016 and 11702315).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yunbo Wan
    • 1
    • 2
  • Nianhua Wang
    • 1
  • Laiping Zhang
    • 1
    • 2
    Email author
  • Yewei Gui
    • 1
    • 2
  1. 1.Stake State Key Laboratory of AerodynamicsChina Aerodynamics Research and Development CenterMianyangChina
  2. 2.Computational Aerodynamics InstituteChina Aerodynamics Research and Development CenterMianyangChina

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