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Developing Hybrid cell-edge and cell-node Dissipative Compact Scheme for Complex Geometry Flows

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Abstract

Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study. High resolution has been achieved by Dissipative Compact Schemes (DCS), however, according to the recent research, applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law (GCL) is not satisfied, and this may cause numerical instability. To cope with this problem, a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme (HDCS) has been formulated. The formulation of the HDCS contains two steps. First, a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL, and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables. The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry, while the DCS may suffer numerical instabilities. Moreover, high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.

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Authors and Affiliations

  1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang, 621000, China

    XiaoGang Deng, Yi Jiang, MeiLiang Mao, HuaYong Liu & GuoHua Tu

  2. National University of Defense Technology, Changsha, 410073, China

    XiaoGang Deng

  3. China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang, 621000, China

    Yi Jiang & MeiLiang Mao

Authors
  1. XiaoGang Deng
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  2. Yi Jiang
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  3. MeiLiang Mao
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  4. HuaYong Liu
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  5. GuoHua Tu
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Correspondence to Yi Jiang.

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Deng, X., Jiang, Y., Mao, M. et al. Developing Hybrid cell-edge and cell-node Dissipative Compact Scheme for Complex Geometry Flows. Sci. China Technol. Sci. 56, 2361–2369 (2013). https://doi.org/10.1007/s11431-013-5339-6

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  • DOI: https://doi.org/10.1007/s11431-013-5339-6

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