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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:302

Review

Zhang, Di¹  Jiang, Chunbo¹  Liang, Dongfang²  Cheng, Liang^3,4 

[1] Tsinghua Univ, State Key Lab Hydrosci & Engn, Beijing 100084, Peoples R China

[2] Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England

[3] Univ Western Australia, Sch Civil Environm & Min Engn, Crawley, WA 6009, Australia

[4] Dalian Univ Technol, State Key Lab Coastal & Offshore Engn, Dalian 116024, Peoples R China

关键词: Total variation diminishing;    High resolution scheme;    Normalized variable diagram;    Convection boundedness criterion;    Convection discretization;    Flux limiter;   

DOI  :  10.1016/j.jcp.2015.08.042

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free