A compact and efficient high-order gas-kinetic scheme
A compact and efficient high-order gas-kinetic scheme
复制标题
紧凑高效的高阶气体动力学方案
DOI：
10.1016/j.jcp.2021.110661
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发表时间：
2021-08
影响因子：
4.1
通讯作者：
Yibing Chen
中科院分区：
文献类型：
--
作者：
Shiyi Li;Dongmi Luo;Jianxian Qiu;Yibing Chen
本文提出了一种紧凑的五阶气体动力学格式（GKS）来求解可压缩流动的欧拉方程。它是基于一种能够在空间和时间上实现任意高阶精度的单级高效高阶GKS （EHGKS）框架，以及结合简单加权基本无振荡格式（WENO）和Hermite基本无振荡格式（HWENO）思想的新开发的紧凑重构技术。EHGKS的演化模型提供了细胞界面的时变变量，可以直接计算细胞平均斜率。从而获得了五阶紧凑HWENO重建技术所需的信息，并通过确定基于紧凑模板的四次多项式将简单WENO改进为紧凑重建。EHGKS的单阶段时间离散化技术使得在每个计算时间步只利用一次重构成为可能，这与目前紧凑的多阶段GKS方案有很大的不同。新开发的紧重构不仅为界面变量的求值提供了点向变量的多项式，而且还提供了它们的空间导数。数值算例验证了所提紧凑单阶段方案的准确性和有效性。数值结果也表明，采用WENO重构技术的EHGKS方法比原方法更有效。
In this paper, a compact fifth-order gas-kinetic scheme (GKS) is proposed to solve the Euler equations of compressible flows. It is based on the framework of a one-stage efficient high-order GKS (EHGKS), which can achieve arbitrary high-order accuracy in both space and time, and the newly-developed compact reconstruction technique, combining both the ideas of the simple weighted essentially non-oscillatory scheme (WENO) and Hermite WENO (HWENO). The evolution model of EHGKS provides the time-dependent variables at cell interfaces, which can directly compute the cell-average slope. Thus the necessary information for a fifth-order compact HWENO reconstruction technique is obtained, and also making it possible to improve simple WENO as a compact reconstruction by determining the quartic polynomial based on the compact stencil. The one-stage time discretization technique of EHGKS makes it possible to utilize the reconstruction only once in each computing time step, which is very different from the present compact multi-stage GKS schemes. The newly-developed compact reconstruction provides the polynomial, not only the pointwise variables but also their spatial derivatives for the interface variables evaluations directly. Several numerical examples are given to validate the accuracy and effectiveness of the proposed compact one-stage scheme. And the numerical results also demonstrate that the new scheme is more efficient than the original EHGKS method with WENO reconstruction technique.
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影响因子：
2.8
作者：
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DOI：
--
发表时间：
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期刊：
--
影响因子：
--
作者：
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通讯作者：
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DOI：
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发表时间：
2013
期刊：
J. Comput. Phys.
影响因子：
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