Compact high order finite volume method on unstructured grids III: Variational reconstruction
Compact high order finite volume method on unstructured grids III: Variational reconstruction
复制标题
非结构化网格上的紧致高阶有限体积法 III：变分重建
DOI：
10.1016/j.jcp.2017.02.031
复制
发表时间：
2017-05
影响因子：
4.1
通讯作者：
Li Wanai
中科院分区：
文献类型：
--
作者：
Wang Qian;Ren Yu-Xin;Pan Jianhua;Li Wanai
本文提出了在任意非结构网格上求解二维N-S方程的高阶有限体积法的变分重构方法。在变分重构中，定义了一个界面跳跃积分来度量重构多项式及其在每个单元界面上的空间导数的跳跃。通过在计算域内用变分方法最小化总界面跳跃积分，得到了确定重构多项式的线性方程组。在每个控制体上，导出的方程是定义在仅涉及当前单元及其直接面邻域的紧凑模板上的重建多项式的系数之间的隐式关系。为了提高计算效率，本文采用了重构与时间积分相结合的迭代方法。采用与问题无关的激波探测器和WBAP限制器来抑制不连续流动模拟中的非物理振荡。本文提出的变分重构有限体积法与本文提出的紧致最小二乘有限体积法相比，具有精度高、计算效率高、边界处理灵活、重构矩阵无奇异性等优点。通过数值算例验证了变分重构有限体积法的精度、效率和激波捕捉能力。
This paper presents a variational reconstruction for the high order finite volume method in solving the two-dimensional Navier–Stokes equations on arbitrary unstructured grids. In the variational reconstruction, an interfacial jump integration is defined to measure the jumps of the reconstruction polynomial and its spatial derivatives on each cell interface. The system of linear equations to determine the reconstruction polynomials is derived by minimizing the total interfacial jump integration in the computational domain using the variational method. On each control volume, the derived equations are implicit relations between the coefficients of the reconstruction polynomials defined on a compact stencil involving only the current cell and its direct face-neighbors. The reconstruction and time integration coupled iteration method proposed in our previous paper is used to achieve high computational efficiency. A problem-independent shock detector and the WBAP limiter are used to suppress non-physical oscillations in the simulation of flow with discontinuities. The advantages of the finite volume method using the variational reconstruction over the compact least-squares finite volume method proposed in our previous papers are higher accuracy, higher computational efficiency, more flexible boundary treatment and non-singularity of the reconstruction matrix. A number of numerical test cases are solved to verify the accuracy, efficiency and shock-capturing capability of the finite volume method using the variational reconstruction.
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影响因子：
2.5
作者：
Z. Wang;Yen Liu;G. May;A. Jameson
通讯作者：
Z. Wang;Yen Liu;G. May;A. Jameson
影响因子：
1.8
作者：
A. Beck;T. Bolemann;David G. Flad;Hannes Frank;G. Gassner;F. Hindenlang;C. Munz
通讯作者：
A. Beck;T. Bolemann;David G. Flad;Hannes Frank;G. Gassner;F. Hindenlang;C. Munz
DOI：
10.2514/6.2010-5093
发表时间：
2010-06
期刊：
--
影响因子：
--
作者：
H. Nishikawa
通讯作者：
H. Nishikawa
DOI：
10.2514/6.1999-3259
发表时间：
1999-11
期刊：
--
影响因子：
--
作者：
M. Delanaye;Yen Liu
通讯作者：
M. Delanaye;Yen Liu
影响因子：
2.8
作者：
R. Abgrall
通讯作者：
R. Abgrall