Extending geometric conservation law to cell-centered finite difference methods on moving and deforming grids
Extending geometric conservation law to cell-centered finite difference methods on moving and deforming grids
复制标题
将几何守恒定律扩展到移动和变形网格上的单元中心有限差分法
DOI：
10.1016/j.jcp.2015.09.032
复制
发表时间：
2015-12
影响因子：
4.1
通讯作者：
Ye, Zhengyin
中科院分区：
文献类型：
--
作者：
Liao, Fei;Ye, Zhengyin
Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al.[8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al.[9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM)[12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al.[11] presented new asymmetric and symmetric conservative forms of time metrics and Jacobian on three-dimensional moving and deforming mesh. Moreover, Abe et al.[14] discussed the symmetrical and asymmetrical geometric interpretations of metrics and Jacobian. By deriving sufficient conditions for the conservative form of VCL, Sjögreen et al.[13] generalized their previous GCL treatment for stationary grids to moving and deforming grids with a new form of time metrics and Jacobian. Recently, Liao et al.[1] focused on the discretization and geometric interpretations of metrics and Jacobian in cell-centered finite difference methods (CCFDM), where the geometric conservation of multiblock interfaces, the treatment of singular axis and simplification of multiblock boundary condition are discussed in detail.The purpose of this note is to extend the treatment of geometric conservation law (GCL) to cell-centered finite difference methods (CCFDMs) on moving and deforming grids as the generalization of the previous work of Liao et al.[1]. In this research, both SCL and VCL identities are considered to compute fluid motion. By investigating the sufficient condition of symmetrical conservative VCL identity, a new evaluation of time metrics is derived with fewer terms to be calculated than the metrics derived by Abe [14] and Sjögreen [13] to further reduce computation cost. The spatial difference is still considered to be half-node to node difference functioning on staggered grid, which represents the transformation process of information. The calculation of Jacobian needs three levels of spatial difference operators to transform coordinate information from grid nodes to grid cell centers. And the calculation of surface metrics and time metrics involves two levels of spatial difference …
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DOI：
10.2514/6.2011-3857
发表时间：
2011-06
期刊：
--
影响因子：
--
作者：
Xiaogang Deng;M. Mao;Yi Jiang;Huayong Liu
通讯作者：
Xiaogang Deng;M. Mao;Yi Jiang;Huayong Liu
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：
--
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
影响因子：
2.5
作者：
P. Thomas;C. Lombard
通讯作者：
P. Thomas;C. Lombard
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
影响因子：
4.1
作者：
Liao, Fei;Ye, Zhengyin;Zhang, Lingxia
通讯作者：
Zhang, Lingxia