Spectral/hp element methods: Recent developments, applications, and perspectives
Spectral/hp element methods: Recent developments, applications, and perspectives
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DOI：
10.1007/s42241-018-0001-1
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发表时间：
2018-02
影响因子：
2.5
通讯作者：
Hui Xu;C. Cantwell;C. Monteserin;C. Eskilsson;A. Engsig-Karup;S. Sherwin
中科院分区：
文献类型：
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作者：
Hui Xu;C. Cantwell;C. Monteserin;C. Eskilsson;A. Engsig-Karup;S. Sherwin
谱/hpelement方法结合了经典h型有限元技术的几何灵活性与谱方法的理想数值特性，在粗糙的有限元型网格上采用高次分段多项式基函数。空间近似是基于正交多项式，如勒让德或切比雪夫多项式，修改，以适应一个C 0连续的扩展。在计算和理论上，通过增加多项式阶数p，可以获得高精度的解和快速收敛，特别是在某些正则性假设下，可以实现数值解和精确解之间的近似误差的指数降低。该方法已应用于许多基本和实际工程流动的模拟研究。本文简要介绍了谱/hpelement方法的公式，并概述了其在计算流体力学中的应用。特别是，它集中在过渡流和海洋工程中的频谱/hpelement方法的使用。最后，为了使用频谱/hpelement方法在更复杂的科学和工程应用中要克服的一些主要挑战进行了讨论。
The spectral/hpelement method combines the geometric flexibility of the classicalh-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate aC0- continuous expansion. Computationally and theoretically, by increasing the polynomial orderp, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hpelement method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hpelement method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hpelement method in more complex science and engineering applications are discussed.