A review on TVD schemes and a refined flux-limiter for steady-state calculations

This paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time–space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time–space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (S...

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Bibliographic Details
Published in:Journal of computational physics 2015-12, Vol.302, p.114-154
Main Authors: Zhang, Di, Jiang, Chunbo, Liang, Dongfang, Cheng, Liang
Format: Article
Language:English
Subjects:
Constraining
Convection boundedness criterion
Convection discretization
Convergence
Criteria
Flux limiter
High resolution scheme
Mathematical analysis
Mathematical models
Normalized variable diagram
Total variation diminishing
TVD schemes
Two dimensional
Unsteady
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Summary:This paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time–space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time–space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (SS-TVD). The design principles of these schemes are examined in detail. It is found that the selection of appropriate flux-limiters is a key design element in developing these schemes. Different flux-limiter forms (CFL-dependent or CFL-independent, and various limiting criteria) are shown to lead to different performances in accuracy and convergence. Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steady-state calculations based on the review. To evaluate the performance of the newly proposed scheme, many existing classical SS-TVD limiters are compared with the TCDF in eight two-dimensional test cases. The numerical results clearly show that the TCDF results in an improved overall performance.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.08.042