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浙江大学学报(工学版)
浙江大学学报(工学版)
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非结构网格下基于梯度光滑法的改进TVD格式
回达, 王双强, 张桂勇, 于大鹏, 宗智
1. 大连理工大学 运载工程与力学学部,辽宁 大连 116024；
2. 大连理工大学 工业装备结构分析国家重点实验室,辽宁 大连 116024
Improved TVD scheme based on gradient smoothing method using unstructured mesh
HUI Da, WANG Shuang-qiang, ZHANG Gui-yong, YU Da-peng, ZONG Zhi
1. Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, School of Naval Architecture, Dalian 116024, China; 
2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology Dalian 116024, China
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摘要：

针对在非结构网格下迎风信息通常无法被清楚地定义而使最小变差递减（TVD）格式很难被直接应用的问题,提出基于梯度光滑法的改进TVD格式.利用基于不同光滑域构造的3种梯度光滑法,即节点梯度光滑法、中点梯度光滑法、中心点梯度光滑法,提出相应的3种改进TVD格式；根据迎风点的位置,先判断所在单元, 然后通过3种改进格式对迎风点上的变量进行插值计算.将提出的改进TVD格式应用于求解双曲型偏微分方程间断问题.在数值实验中，采用3种经典流通量限制器（Superbee,Van Leer和Minmod），并将结果与其他方法相比.数值结果表明,基于梯度光滑法的改进TVD格式能够有效避免数值振荡,并减小数值耗散,对于间断问题和连续问题均取得较好的计算结果.
Abstract: Generally upwind information cannot be clearly defined on unstructured mesh, thus a total variation diminishing (TVD) is difficult to be directly applied in such a mesh. An improved TVD scheme was proposed based on the gradient smoothing method (GSM) using unstructured mesh in order to solve the above problem. Using different smoothing domains, there are three types of GSM, i.e. node gradient smoothing method (nGSM)、midpoint gradient smoothing method (mGSM) and centre gradient smoothing method (cGSM). According to the above GSM models, three types of improved TVD were developed. In each scheme, locations of upwind points were to be found out and the variables at these points were calculated through interpolation operation. The improved TVD schemes were used to solve hyperbolic partial differential equation discontinuous problems and the results were compared with those by other methods, where three classical flux limiters (Superbee, Van leer and Minmod) were used. Numerical results show that the improved TVD based on GSM can effectively avoid the numerical oscillation and reduce the numerical diffusion, which can obtain good numerical results for both continuous and discontinuous problems.
出版日期: 2017-05-01
CLC:  O 241.82  
基金资助:

青年千人计划资助项目（D1007001）；国家自然科学基金资助项目（51579042）；中央高校基本科研业务费专项基金资助项目（DUT16ZD218）.
通讯作者: 张桂勇,男,教授,博导. ORCID: 0000-0002-6569-6286. 主要从事计算船舶力学等研究.     E-mail: gyzhang@dlut.edu.cn
作者简介: 回达（1989—）,男,博士生,主要从事计算流体力学方面等研究. ORCID: 0000-0003-4747-8944. E-mail: huida_answer@hotmail.com
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引用本文:

回达, 王双强, 张桂勇, 于大鹏, 宗智. 非结构网格下基于梯度光滑法的改进TVD格式[J]. 浙江大学学报(工学版), 10.3785/j.issn.1008-973X.2017.05.025.

HUI Da, WANG Shuang-qiang, ZHANG Gui-yong, YU Da-peng, ZONG Zhi. Improved TVD scheme based on gradient smoothing method using unstructured mesh. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 10.3785/j.issn.1008-973X.2017.05.025.

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