Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2016, Vol. 33 ›› Issue (6): 578-586.doi: 10.3969/j.issn.1005-3085.2016.06.002

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The Modified High-resolution Composite Scheme Based on the Leonard Normalized Variable

NIU Yun-xia1,2, LI Chun-guang3, JING He-fang3   

  1. 1. School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021
    2. Xinjiang University Institute of Science and Technology (Akesu Campus), Akesu 843000
    3. Research Institute of Numerical Computation and Engineering Applications, Beifang University of Nationalities, Yinchuan 750021
  • Received:2015-04-07 Accepted:2015-12-01 Online:2016-12-15 Published:2017-02-15
  • Contact: C. Li. E-mail address: cglizd@hotmail.com
  • Supported by:
    The National Natural Science Foundation of China (11361002); the Ningxia Water Resources Project ([2015]50-18); the Graduate Student Innovation Projects of Beifang University of Nation-alities (YCX1555); the Graduate Student Innovation Projects of School of Mathematics and Information Science of Beifang University of Nationalities.

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Abstract: Based on the normalized variable, a modified high-resolution composite scheme is proposed to solve the convection-diffusion equation, which can be used to describe boundary layer problems or locally large gradient problems. Firstly, the generic form for the composite scheme is derived according to the definition of the normalized variable. Then, the second order central difference scheme is used to discretize the temporal derivative term. The discrete algebraic equations are solved with the TDMA algorithm. Thus, the sufficient condition for the convergence of the composite scheme is obtained. The numerical tests are presented to verify the effectiveness of the scheme. The numerical results show that the new format has higher resolution, lower numerical dissipation and smaller total amount of deviation when compared with traditional formats. The new scheme is good at simulating the large gradient field variables.

Key words: convection-diffusion equation, high-resolution combination scheme, Leonard normalized variable, TDMA algorithm

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