Further Study on Errors inMetric Evaluation by Linear Upwind Schemes with Flux Splitting in Stationary Grids
Further Study on Errors inMetric Evaluation by Linear Upwind Schemes with Flux Splitting in Stationary Grids
复制标题
固定网格磁通分裂线性迎风方案度量评价误差的进一步研究
DOI：
10.4208/cicp.oa-2016-0123
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
Pengxin Liu
中科院分区：
文献类型：
--
作者：
Qin Li;Dong Sun;Pengxin Liu
近年来，消除高阶差分格式的网格度量评估中的误差的重要性已被广泛认识，并且从 Vinokur 和 Yee (NASA TM 209598, 2000) 的证明可知，当 Thomas、Lombard 和 Neier 使用网格度量的保守推导时 (AIAA J., 1978, 17(10) 和 J. Spacecraft and Rocket, 1990, 27（2）），当不考虑通量分裂时，由度量评估引起的误差可以通过线性方案消除。根据上述成果，不使用通量分裂的中心方案可以满足误差消除的要求。当考虑到分裂时，迎风方案要实现目标将会遇到困难。本研究在三个方面进行了进一步的研究：首先，引入了中心方案分解的思想，并提出了仅评估网格指标的中心方案的推导过程。其次，分析了通量分裂获得自由流保持的要求，并以Lax-Friedrichs型分裂方案为例提出了方案。关于当前研究与野野村等人的讨论。 （计算机和流体，2015，107）已经完成。第三，对于半节点或混合型方案，应使用插值来导出半节点处的变量。分析了这种情况下实现度量同一性的要求，并提出了方向一致插值的思想，这对于避免违反度量同一性和消除度量引起的错误是必不可少的。测试了两个数值问题，即波浪状、很大程度上随机和三角形网格上的自由流和涡流保持。数值结果验证了上述理论结果。
The importance of eliminating errors in grid-metric evaluation for high order difference schemes has been widely recognized in recent years, and it is known from the proof by Vinokur and Yee (NASA TM 209598, 2000) that when conservative derivations of grid metric are used by Thomas, Lombard and Neier (AIAA J., 1978, 17(10) and J. Spacecraft and rocket, 1990, 27(2)), errors caused by metric evaluation could be eliminated by linear schemes when flux splitting is not considered. According to the above achievement, central schemes without the use of flux splitting could fulfill the requirement of error elimination. Difficulties will arise for upwind schemes to attain the objective when the splitting is considered. In this study, further investigations are made on three aspects: Firstly, an idea of central scheme decomposition is introduced, and the procedure to derive the central scheme is proposed to evaluate grid metrics only. Secondly, the analysis has been made on the requirement of flux splitting to acquire free-stream preservation, and a Lax-Friedrichs-type splitting scheme is proposed as an example. Discussions about current study with that by Nonomura et al. (Computers and Fluids, 2015, 107) have been made. Thirdly, for half node or mixed-type schemes, interpolations should be used to derive variables at half nodes. The requirement to achieve metric identity on this situation is analyzed and an idea of directionally consistent interpolation is proposed, which is manifested to be indispensable to avoid violations of metric identity and to eliminate metric-caused errors thereafter. Two numerical problems are tested, i.e., the free-stream and vortex preservation on wavy, largely randomized and triangular-like grids. Numerical results validate aforementioned theoretical outcomes.