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Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

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Abstract

Discontinuous Galerkin (DG) method is known to have several advantages for flow simulations, in particular, in flexible accuracy management and adaptability to mesh refinement. In the present work, the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer, both the instantaneous flow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer, large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous flow field for a three-dimensional compressible mixing layer is also reported, which shows the development of large-scale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear flows.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems and Dept. Mechanical and Aerospace Engineering, College of Engineering, Peking University, 100871, Beijing, China

    Xiao-Tian Shi, Jun Chen, Wei-Tao Bi & Zhen-Su She

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

Authors
  1. Xiao-Tian Shi
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  2. Jun Chen
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  3. Wei-Tao Bi
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  4. Chi-Wang Shu
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  5. Zhen-Su She
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Correspondence to Zhen-Su She.

Additional information

The project was supported by the National Natural Science Foundation of China (90716008,10572004 and 10921202), MOST 973 Project (2009CB724100) and CSSA.

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Shi, XT., Chen, J., Bi, WT. et al. Numerical simulations of compressible mixing layers with a discontinuous Galerkin method. Acta Mech Sin 27, 318–329 (2011). https://doi.org/10.1007/s10409-011-0433-0

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  • DOI: https://doi.org/10.1007/s10409-011-0433-0

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