SCIENCE CHINA Information Sciences, Volume 63 , Issue 6 : 164101(2020) https://doi.org/10.1007/s11432-018-9889-8

Detail-preserving smoke simulation using an efficient high-order numerical scheme

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  • ReceivedDec 7, 2018
  • AcceptedApr 1, 2019
  • PublishedAug 27, 2019


There is no abstract available for this article.


This work was supported by National Natural Science Foundation of China (Grant Nos. 61502109, 61672502, 61402038), Natural Science Foundation of Guangdong Province (Grant Nos. 2016A030310342, 2018A030313802), National Key RD Program of China (Grant No. 2017YFB1002701), Science and Technology Planning Project of Guangdong Province (Grant Nos. 2017B010110015, 2017B010110007), Open Research Fund of Guangdong Provincial Key Laboratory of Cyber-Physical System (Grant No. 2016B030301008).


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  • Figure 1

    (Color online) Illustration of the proposed Taylor expansion-based CIP in 2D.


    Algorithm 1 Taylor expansion-based CIP in 2D

    Require:${[\phi~,{\partial~_x}\phi~,{\partial~_y}\phi]}$ at A, B, C, D;

    Output:${[\phi~,{\partial~_x}\phi~,{\partial~_y}\phi]}$ at P.

    Compute ${\partial~_{xy}}{\phi}$ at A, B, C, D by Eqs. 25;

    Compute ${[\phi~,{\partial~_x}\phi~]_{\rm~E}}$ from ${[\phi~,{\partial~_x}\phi~]_{\rm~A}}$ and ${[\phi~,{\partial~_x}\phi~]_{\rm~B}}$ by 1D CIP interpolation;

    Compute ${[{\partial~_y}\phi~,{\partial~_{xy}}\phi~]_{\rm~E}}$ from ${[{\partial~_y}\phi~,{\partial~_{xy}}\phi~]_{\rm~A}}$ and $[{\partial~_y}\phi~,$ ${\partial~_{xy}}\phi~]_{\rm~B}$ by 1D CIP interpolation;

    Compute ${[\phi~,{\partial~_x}\phi~]_{\rm~F}}$ from ${[\phi~,{\partial~_x}\phi~]_{\rm~D}}$ and ${[\phi~,{\partial~_x}\phi~]_{\rm~C}}$ by 1D CIP interpolation;

    Compute ${[{\partial~_y}\phi~,{\partial~_{xy}}\phi~]_{\rm~F}}$ from ${[{\partial~_y}\phi~,{\partial~_{xy}}\phi~]_{\rm~D}}$ and $[{\partial~_y}\phi,$ ${\partial~_{xy}}\phi~]_{\rm~C}$ by 1D CIP interpolation;

    Compute ${[\phi~,{\partial~_y}\phi~]_{\rm~P}}$ from ${[\phi~,{\partial~_y}\phi~]_{\rm~E}}$ and ${[\phi~,{\partial~_y}\phi~]_{\rm~F}}$ by 1D CIP interpolation;

    Compute ${[{\partial~_x}\phi~,{\partial~_{xy}}\phi~]_{\rm~P}}$ from ${[{\partial~_x}\phi~,{\partial~_{xy}}\phi~]_{\rm~E}}$ and $[{\partial~_x}\phi,$ ${\partial~_{xy}}\phi~]_{\rm~F}$ by 1D CIP interpolation.

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