Effects of difference scheme type in high-order weighted compact nonlinear schemes
Effects of difference scheme type in high-order weighted compact nonlinear schemes
复制标题
DOI：
10.1016/j.jcp.2009.02.018
复制
发表时间：
2009-06
期刊：
影响因子：
--
通讯作者：
T. Nonomura;K. Fujii
中科院分区：
文献类型：
--
作者：
T. Nonomura;K. Fujii
加权紧致非线性格式（WCNS）是由Deng和Zhang [1]发展起来的一种求解含间断流场的高分辨率格式。Deng和Zhang证明了WCNS比有限差分加权基本无振荡格式（韦诺）[2]具有略高的分辨率和与韦诺相似的间断捕捉能力。与韦诺相比，WCNS具有以下三个优点：（1）可以使用各种通量分裂方法，例如Roe的通量差分裂方法（FDS）[3];（2）尽管采用有限差分公式，但可以使用流动变量的插值;（3）波浪网格上的自由振荡和涡保持特性非常好[4]。到目前为止，高阶WCNS已经由Nonomura等人开发。[5]和Zhang等人[6]Zhang等人提出了用插值通量代替原始版本和Nonomura等人开发的高阶版本中使用的保守变量。这些研究表明，分辨率随着精度阶数的增加而增加，高阶WCNS更有效。WCNS程序由三个部分组成[1]：（1）保守变量的单元节点到单元中心的加权平均插值，（2）单元中心的通量评估和（3）单元中心到单元节点的差分。在第三分量中，各种类型的小区中心到小区节点差分方案可用。Deng和Zhang表明，细胞中心到细胞节点差分方案的类型，显式或三对角，不会影响五阶或四阶WCNS的分辨率，因为加权平均插值（分量1）对其分辨率起主导作用[7]。0021 -9991/$-参见前页© 2009 Elsevier Inc. All rights reserved. doi：10.1016/j. jcp. 2009.02. 018
The weighted compact nonlinear scheme (WCNS), developed by Deng and Zhang [1], is a high resolution scheme for flow fields including discontinuities. Deng and Zhang showed that WCNS has slightly higher resolution than the finite difference weighted essentially non-oscillatory scheme (WENO)[2] and similar discontinuity capturing capability as WENO. WCNS has the following three advantages compared with WENO:(1) various flux splitting methods can be used, eg Roe’s flux difference splitting method (FDS)[3];(2) interpolation of flow variables can be used despite the finite difference formulation; and (3) freestream and vortex preservation properties are very good on a wavy grid [4]. Thus far, the higher-order WCNSs have been developed by Nonomura et al.[5] and Zhang et al.[6] up to the ninth-order, while Zhang et al. proposed interpolating flux instead of the conservative variables used both in the original version and in the higher-order version developed by Nonomura et al. These researches showed that the resolution increases with an increasing order of accuracy and higher-order WCNSs are much more effective. The WCNS procedure consists of three components [1]:(1) cell-node to cell-center weighted averaging interpolation of conservative variables,(2) flux evaluation at the cell-center and (3) cell-center to cell-node differencing. In the third component, various types of the cell-center to cell-node difference schemes are available. Deng and Zhang showed that the type of cell-center to cell-node difference scheme, explicit or tri-diagonal, does not affect the resolution of a fifth-order or fourthorder WCNS, because the weighted averaging interpolation (component 1) is dominant for its resolution [7].0021-9991/$-see front matter© 2009 Elsevier Inc. All rights reserved. doi: 10.1016/j. jcp. 2009.02. 018