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China Ocean Engineering

, Volume 30, Issue 4, pp 615–626 | Cite as

Comparison and modification: TVD schemes for scalar transport on an unstructured grid

  • Zhuo Zhang (张 卓)
  • Zhi-yao Song (宋志尧)Email author
  • Fei Guo (郭 飞)
  • Dong Zhang (张 东)
  • Yong-ning Wen (温永宁)
  • Di Hu (胡 迪)
Article
  • 58 Downloads

Abstract

In most TVD schemes, the r-factors were proposed according to the cell-centered (CC) finite volume method (FVM) framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered (VC) FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner (1996), Darwish and Moukalled (2003) and Cassuli and Zanolli (2005) can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely ϕ U in the paper, was validated by the tests to effectively dissipate spurious oscillations.

Key words

TVD scheme unstructured grid vertex-centered FVM flux limiter r-factor 

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Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Zhuo Zhang (张 卓)
    • 1
    • 2
  • Zhi-yao Song (宋志尧)
    • 1
    • 2
    • 3
    Email author
  • Fei Guo (郭 飞)
    • 1
    • 2
  • Dong Zhang (张 东)
    • 1
    • 2
  • Yong-ning Wen (温永宁)
    • 1
    • 2
  • Di Hu (胡 迪)
    • 1
    • 2
  1. 1.Key Lab of Virtual Geographic Environment under Ministry of EducationNanjing Normal UniversityNanjingChina
  2. 2.Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and ApplicationNanjing Normal UniversityNanjingChina
  3. 3.Jiangsu Key Lab for Numerical Simulation of Large-Scale Complex SystemNanjing Normal UniversityNanjingChina

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