Compact-WENO杂交格式中旋涡识别的多分辨率分析方法

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英文篇名：Vortex Identification Based Multi-Resolution Analysis for Hybrid Compact-WENO Scheme 作者：王保山 ; 曾维新 ; 高振 ; 陈玉虎 英文作者：WANG Bao-Shan;DON Wai-Sun;GAO Zhen;CHEN Yu-Hu;School of Mathematical Sciences,Ocean University of China;Pilot National Laboratory for Marine Science and Technology(Qingdao); 关键词：旋涡识别 ; 多分辨率分析 ; WENO-Z格式 ; 杂交格式 英文关键词：vortex identification;;multi-resolution analysis;;WENO-Z scheme;;Hybrid scheme 中文刊名：QDHY 英文刊名：Periodical of Ocean University of China 机构：中国海洋大学数学科学学院;青岛海洋科学与技术试点国家实验室; 出版日期：2018-12-10 出版单位：中国海洋大学学报(自然科学版) 年：2018 期：v.48;No.289 基金：国家自然科学基金项目(11871443);; 山东省自然科学基金项目(ZR2017MA016);; 中央高校基本科研业务费专项项目(201562012);; 国家重大科技专项(20101010)资助~~ 语种：中文; 页：QDHY2018S2026 页数：5 CN：S2 ISSN：37-1414/P 分类号：201-205

摘要

在Compact-WENO杂交格式中,判定流场中解的光滑性、设计间断检测算法是最为关键的部分。对于高维问题,已有的间断检测算法,如多分辨率分析(MR)方法,通常采用维数分裂的方法进行间断的捕捉,往往将湍流中光滑的旋涡结构误判为间断,从而导致杂交格式无法准确地求解这些细小的旋涡结构。本文基于流场中的散度和旋度,改进了多分辨率分析的系数,使得旋涡处的系数接近于零,从而避免MR方法对旋涡结构的误判。几个典型的二维数值模拟表明,改进后的多分辨率分析方法能够准确地识别间断结构和光滑的旋涡结构,结合新方法的杂交格式比五阶WENO-Z格式的效率高2~3倍。
        The key issue in Hybrid Compact-WENO scheme is the design of the high order shocks detection algorithm which is capable of determining the smoothness of the solution at any given grid point and time.When applied to high-dimensional problems by the dimension-by-dimension approach,the existing shocks detection algorithms,such as the multi-resolution(MR)analysis,might misidentify the smooth vortex structures in turbulent flow simulations as the high gradients/discontinuities.Consequently,the Hybrid Compact-WENO scheme cannot resolve these finite vortex structures exactly.In this work,we improve the MR coefficients by using the divergence and curl in the flow field to vanish at the vortex and overcome above issue.Several two-dimensional benchmark problems in shocked flow demonstrate that the improved MR analysis performs very well in shocks capturing and vortex identification and the corresponding Hybrid scheme can reach a speedup of the CPU times by the factor up to 2~3 compared with the pure fifth order WENO-Z scheme.

引文

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