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A compact and efficient high-order gas-kinetic scheme
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-08-24 , DOI: 10.1016/j.jcp.2021.110661
Shiyi Li , Dongmi Luo , Jianxian Qiu , Yibing Chen

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.



中文翻译:

一种紧凑高效的高阶气体动力学方案

在本文中,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。它基于可以在空间和时间上实现任意高阶精度的单级高效高阶GKS(EHGKS)框架和新开发的紧凑重构技术,结合了简单的思想加权基本非振荡方案 (WENO) 和 Hermite WENO (HWENO)。EHGKS 的演化模型提供了单元界面处的时间相关变量,可以直接计算单元平均斜率。因此,获得了五阶紧凑 HWENO 重建技术的必要信息,并且还可以通过基于紧凑模板确定四次多项式来改进简单 WENO 作为紧凑重建。EHGKS 的单级时间离散化技术使得在每个计算时间步仅使用一次重构成为可能,这与目前紧凑的多级 GKS 方案有很大不同。新开发的紧凑重建提供多项式,不仅是逐点变量,还提供它们的空间导数,用于直接评估界面变量。给出了几个数值例子来验证所提出的紧凑一级方案的准确性和有效性。数值结果也表明新方案比采用WENO重建技术的原始EHGKS方法更有效。新开发的紧凑重建提供多项式,不仅是逐点变量,还提供它们的空间导数,用于直接评估界面变量。给出了几个数值例子来验证所提出的紧凑一级方案的准确性和有效性。数值结果也表明新方案比采用WENO重建技术的原始EHGKS方法更有效。新开发的紧凑重建提供多项式,不仅是逐点变量,还提供它们的空间导数,用于直接评估界面变量。给出了几个数值例子来验证所提出的紧凑一级方案的准确性和有效性。数值结果也表明新方案比采用WENO重建技术的原始EHGKS方法更有效。

更新日期:2021-09-12
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