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

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• 作者：Di Zhang^a ; ^{zhangdi10@mails.tsinghua.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Chunbo Jiang^a ; ^{jcb@mail.tsinghua.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dongfang Liang^b ; Liang Cheng^c ; ^d
• 关键词：Total variation diminishing ; High resolution scheme ; Normalized variable diagram ; Convection boundedness criterion ; Convection discretization ; Flux limiter
• 刊名：Journal of Computational Physics
• 出版年：2015
• 出版时间：1 December 2015
• 年：2015
• 卷：302
• 期：Complete
• 页码：114-154
• 全文大小：9836 K

文摘

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.