High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions
High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions
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欧拉和纳维-斯托克斯解的三维 WENO 重建高阶气体动力学方案
DOI：
10.1016/j.compfluid.2019.104401
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发表时间：
2019-09
影响因子：
2.8
通讯作者：
Kun Xu
中科院分区：
文献类型：
--
作者：
Pan Liang;Kun Xu
本文采用非结构网格上二维WENO-AO格式的思想，发展了一种简单有效的三维流动的三阶加权基本无振荡（韦诺）重建方法。在经典的有限体积型韦诺格式中，候选项的线性权系数是通过求解细胞界面高斯求积点处的线性方程组来获得的。对于三维格式，在六面体的24个高斯正交点上进行这种操作会大大降低效率，特别是对于移动网格计算。经典韦诺格式的另一个缺点是会出现局部拓扑不规则的负权值，影响了空间重构的鲁棒性。对于三维WENO-AO格式，提出了一种简单的选择大模板和子模板进行重建的策略。利用大模板重构的二次多项式和子模板重构的线性多项式，选择线性权值为正数，并要求其和等于1且与局部网格拓扑无关。基于韦诺格式，本文发展了一种适用于三维无粘和粘性流动的高阶气体动力学格式。在考虑网格速度的情况下，将该格式推广到动网格计算中。数值结果表明，这种新的有限体积韦诺格式的良好性能。在未来，这种韦诺重建将扩展到非结构网格。
In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes [42] is adopted. In the classical finite volume type WENO schemes, the linear weights for candidate stencils are obtained by solving linear systems at Gaussian quadrature points of cell interface. For the three-dimensional scheme, such operations at twenty-four Gaussian quadrature points of a hexahedron would reduce the efficiency greatly, especially for the moving-mesh computation. Another drawback of the classical WENO schemes is the appearance of negative weights with irregular local topology, which affect the robustness of spatial reconstruction. For the three-dimensional WENO-AO scheme, a simple strategy of selecting big stencil and sub-stencils for reconstruction is proposed. With the reconstructed quadratic polynomial from big stencil and linear polynomials from sub-stencils, the linear weights are chosen as positive numbers with the requirement that their summation equals to one and be independent of local mesh topology. With such WENO reconstruction, a high-order gas-kinetic scheme (HGKS) is developed for both three-dimensional inviscid and viscous flows. Taken the grid velocity into account, the scheme is extended into the moving-mesh computation as well. Numerical results are provided to illustrate the good performance of such new finite volume WENO scheme. In the future, such WENO reconstruction will be extended to the unstructured meshes.
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影响因子：
64.8
作者：
R. H. Fowler
通讯作者：
R. H. Fowler
DOI：
10.1016/j.jcp.2006.06.043
发表时间：
2007-02
期刊：
J. Comput. Phys.
影响因子：
--
作者：
M. Dumbser;M. Käser
通讯作者：
M. Dumbser;M. Käser
影响因子：
4.1
作者：
HARTEN, A;ENGQUIST, B;CHAKRAVARTHY, SR
通讯作者：
CHAKRAVARTHY, SR
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
DOI：
10.1137/15m1052512
发表时间：
2015-12
期刊：
SIAM J. Sci. Comput.
影响因子：
--
作者：
Jiequan Li;Zhifang Du
通讯作者：
Jiequan Li;Zhifang Du