A refined r-factor algorithm for TVD schemes on arbitrary unstructured meshes
Authors
Zhang, Di
Jiang, Chunbo
Cheng, Liang
Liang, Dongfang
Publication Date
2015-07-03Journal Title
International Journal for Numerical Methods in Fluids
ISSN
0271-2091
Publisher
Wiley
Language
English
Type
Article
Metadata
Show full item recordCitation
Zhang, D., Jiang, C., Cheng, L., & Liang, D. (2015). A refined r-factor algorithm for TVD schemes on arbitrary unstructured meshes. International Journal for Numerical Methods in Fluids https://doi.org/10.1002/fld.4073
Abstract
A refined r-factor algorithm for implementing TVD schemes on arbitrary unstructured meshes, referred to henceforth as FFISAM (a Face-perpendicular Far-upwind Interpolation Scheme for Arbitrary Meshes), is proposed based on an extensive review of the existing r-factor algorithms available in the literature. The design principles, as well as the respective advantages and disadvantages, of the existing algorithms are first systematically analyzed before presenting the FFISAM. The FFISAM is designed to combine the merits of various existing r-factor algorithms. The performance of the FFISAM, implemented in ten classical TVD schemes, is evaluated against four two-dimensional pure-advection benchmark test cases where analytical solutions are available. The numerical results clearly show that the FFISAM leads to a better overall performance than the existing algorithms in terms of accuracy and convergence on arbitrary unstructured meshes for the ten classical TVD schemes.
Keywords
total variation diminishing (TVD), high resolution scheme (HRS), normalized variable diagram (NVD), r-factor algorithm, convection discretization, unstructured meshes
Sponsorship
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51279082) and the support from Australian Research Council through a Discovery Grant (Project ID: DP110105171).
Identifiers
External DOI: https://doi.org/10.1002/fld.4073
This record's URL: https://www.repository.cam.ac.uk/handle/1810/249009
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