A review on TVD schemes and a refined flux-limiter for steady-state calculations
Journal of Computational Physics
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Zhang, D., Jiang, C., Liang, D., & Cheng, L. (2015). A review on TVD schemes and a refined flux-limiter for steady-state calculations. Journal of Computational Physics, 302 114-154. https://doi.org/10.1016/j.jcp.2015.08.042
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 steadystate 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.
total variation diminishing, high resolution scheme, normalized variable diagram, convection boundedness criterion, convection discretization, flux limiter
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51279082 and 51511130073) and the support from Australian Research Council through a Discovery Grant (Project ID: DP110105171).
External DOI: https://doi.org/10.1016/j.jcp.2015.08.042
This record's URL: https://www.repository.cam.ac.uk/handle/1810/250531