A refined r-factor algorithm for TVD schemes on arbitrary unstructured meshes

• Published in: International journal for numerical methods in fluids Vol. 80; no. 2; pp. 105 - 139
• Main Authors: Zhang, Di, Jiang, Chunbo, Cheng, Liang, Liang, Dongfang
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 20.01.2016; Wiley Subscription Services, Inc
• Subjects: Accuracy; Algorithms; Computational fluid dynamics; convection discretization; Convergence; high-resolution scheme (HRS); Interpolation; Mathematical models; normalized variable diagram (NVD); Preserves; r-factor algorithm; total variation diminishing (TVD); TVD schemes; unstructured meshes
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4073

Summary A refined r‐factor algorithm for implementing total variation diminishing (TVD) schemes on arbitrary unstructured meshes, referred to henceforth as a face‐perpendicular far‐upwind interpolation scheme for arbitrary meshes (FFISAM), 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 10 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 10 classical TVD schemes. Copyright © 2015 John Wiley & Sons, Ltd. The key findings: Several existing r‐factor algorithms available in the literature are reviewed in detail for extending TVD schemes to arbitrary unstructured grids, and the respective advantages and disadvantages of these algorithms are also revealed and analyzed. A refined r‐factor algorithm (FFISAM) is proposed based on the review. The FFISAM is designed to overcome several inherent drawbacks of the existing algorithms while preserve their attractive attributes. Numerical results show that the FFISAM leads to a better performance in terms of accuracy and convergence.