吕宏强, 张涛, 孙强, 陈建伟, 秦望龙. 间断伽辽金方法在可压缩流数值模拟中的应用研究综述[J]. 空气动力学学报, 2017, 35(4): 455-471. DOI: 10.7638/kqdlxxb-2017.0051
引用本文: 吕宏强, 张涛, 孙强, 陈建伟, 秦望龙. 间断伽辽金方法在可压缩流数值模拟中的应用研究综述[J]. 空气动力学学报, 2017, 35(4): 455-471. DOI: 10.7638/kqdlxxb-2017.0051
LYU Hongqiang, ZHANG Tao, SUN Qiang, CHEN Jianwei, QIN Wanglong. Applications of discontinuous Galerkin method in numerical simulations of compressible flows:A review[J]. ACTA AERODYNAMICA SINICA, 2017, 35(4): 455-471. DOI: 10.7638/kqdlxxb-2017.0051
Citation: LYU Hongqiang, ZHANG Tao, SUN Qiang, CHEN Jianwei, QIN Wanglong. Applications of discontinuous Galerkin method in numerical simulations of compressible flows:A review[J]. ACTA AERODYNAMICA SINICA, 2017, 35(4): 455-471. DOI: 10.7638/kqdlxxb-2017.0051

间断伽辽金方法在可压缩流数值模拟中的应用研究综述

Applications of discontinuous Galerkin method in numerical simulations of compressible flows:A review

  • 摘要: 本文对近三十年来,国内外对于高精度数值方法研究中的热点——间断伽辽金方法在可压缩流数值模拟方面的应用研究进行了综述。首先对间断伽辽金方法的基本概念和特点作了简单介绍,然后对应用该方法解决双曲型及椭圆型问题的发展历程进行了回顾,并重点梳理了其在计算流体力学领域可压缩流数值模拟方面的应用发展以及研究现状,之后对该方法在对应的网格技术、激波捕捉方法、湍流流动模拟以及计算量需求方面目前仍然存在的研究难点和可能的发展趋势做出了总结和分析。最后给出了间断伽辽金方法在可压缩流数值模拟中的若干应用实例。

     

    Abstract: In this paper, we give a review on the international and domestic applications of the promising high-order method(HOM), the discontinuous Galerkin method (DGM), in the numerical simulation of compressible flows over the last three decades. A brief introduction of the basic concepts and attributes of the DGM is given first. Then a historical survey on the DGM's applications in solving hyperbolic and elliptical equations is presented, mainly concentrating on its development and research status in the field of computational fluid dynamics (CFD). Existing challenges and possible trends in the aspects of corresponding mesh technologies, shockwave capturing methods, turbulence simulation, and computational resource requirement are concluded and analyzed as well. Several examples of its applications in the simulation of compressible flows are provided at last.

     

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