Comparison and Modification: TVD Schemes for Scalar Transport onAn Unstructured Grid |
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Authors: | ZHANG Zhuo SONG Zhi-yao GUO Fei ZHANG Dong WEN Yong-ning HU Di |
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Affiliation: | Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China;Key Lab of Virtual Geographic Environment under Ministry of Education, Nanjing Normal University,Nanjing 210023, China |
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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 in the paper, was validated by the tests to effectively dissipate spurious oscillations. |
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Keywords: | TVD scheme unstructured grid vertex-centered FVM flux limiter r-factor |
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