Extending geometric conservation law to cell-centered finite difference methods on stationary grids
Extending geometric conservation law to cell-centered finite difference methods on stationary grids
复制标题
将几何守恒定律扩展到固定网格上的单元中心有限差分法
DOI：
10.1016/j.jcp.2014.12.040
复制
发表时间：
2015-03
影响因子：
4.1
通讯作者：
Zhang, Lingxia
中科院分区：
文献类型：
--
作者：
Liao, Fei;Ye, Zhengyin;Zhang, Lingxia
In a wide range of high-order high-resolution schemes, the finite difference method (FDM) is a suitable selection for accurate numerical calculations because it efficiently reduces dispersion and dissipation errors. FDM is easier to perform to obtain high-order capabilities than the finite volume method (FVM). Most FDMs are node-centered; such techniques include weighted essentially non-oscillatory schemes (WENO)[1], weighted compact nonlinear schemes (WCNS)[2],[3], dissipative compact schemes (DCS)[4], and compact central schemes [5],[6]. WENO represents a class of nonlinear high-order high-resolution shock-capture schemes derived by Shu [1]; this technique can be successfully used in multiscale flow simulation problems. WCNS is another nonlinear high-order shock-capture scheme derived by Deng and Zhang. WCNS uses interpolation and not reconstruction to obtain half-node values and features a better spectral resolution than WENO. Deng et al.[4] further developed linear DCS with a free parameter to control upwind tendency and thus decrease the dissipation of upwind schemes. Furthermore, compact central scheme proposed by Lele [5] and developed by Visbal and Gaitonde [6] plays a dominant role for research on large eddy simulation and direct numerical simulation because of its ultra-high-order and spectral-like resolution.Geometric conservation law (GCL) identities, including surface conservation law (SCL) and volume conservation law (VCL), are important in high-order FDM to ensure free-stream preservation. Unsatisfied GCL results in incorrect convective terms and extra source or sink in flow fields, leading to numerical inaccuracy, instabilities, or even blow up, particularly in high-order schemes. Visbal and Gaitonde [6] extended GCL to high-order compact central schemes by using the conservative form of metrics derived by Thomas and Lombard [7]. Investigating free stream and vortex preservation properties, Nonomura et al.[9] demonstrated that GCL can be satisfied through WCNS by using conservative metrics. A conservative metric method (CMM) was further developed by Deng et al.[10] and was successfully applied to WCNS-E-5 and modified DCS5. A symmetrical CMM (SCMM) was proposed by Abe et al.[12] in 2012 and Deng et al.[13] in 2013 by using the symmetric forms of metrics derived by Vinokur [11] to further eliminate asymmetric metric errors. Sjögreen et al.[14] have recently generalized their previous GCL treatment for stationary grids to moving grids. Moreover, Abe et al.[15] derived sufficient conditions for the conservative form of GCL and focused on the symmetrical and asymmetrical properties of metrics, particularly in geometric interpretations.
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DOI：
10.1016/j.jcp.2014.01.045
发表时间：
2014-05
期刊：
J. Comput. Phys.
影响因子：
--
作者：
B. Sjögreen;H. C. Yee;M. Vinokur
通讯作者：
B. Sjögreen;H. C. Yee;M. Vinokur
DOI：
10.2514/6.1997-1941
发表时间：
1997-06
期刊：
--
影响因子：
--
作者：
Xiaogang Deng;M. Mao
通讯作者：
Xiaogang Deng;M. Mao
DOI：
--
发表时间：
2012
期刊：
--
影响因子：
--
作者：
Yoshiaki Abe;N. Iizuka;T. Nonomura;K. Fujii
通讯作者：
Yoshiaki Abe;N. Iizuka;T. Nonomura;K. Fujii
气动弹性效应对风洞数据散射现象的影响
DOI：
10.1007/s11431-012-5100-6
发表时间：
2013-02
期刊：
Science China: Technological Science
影响因子：
--
作者：
叶正寅,蒋跃文,周乃桢
通讯作者：
叶正寅,蒋跃文,周乃桢
影响因子：
2.5
作者：
P. Thomas;C. Lombard
通讯作者：
P. Thomas;C. Lombard