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张涵信, 呙超, 宗文刚. 网格与高精度差分计算问题[J]. 力学学报, 1999, 31(4): 398-405. DOI: 10.6052/0459-1879-1999-4-1995-047
引用本文: 张涵信, 呙超, 宗文刚. 网格与高精度差分计算问题[J]. 力学学报, 1999, 31(4): 398-405. DOI: 10.6052/0459-1879-1999-4-1995-047
PROBLEMS ABOUT GIRD AND HIGH ORDER SCHEMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(4): 398-405. DOI: 10.6052/0459-1879-1999-4-1995-047
Citation: PROBLEMS ABOUT GIRD AND HIGH ORDER SCHEMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(4): 398-405. DOI: 10.6052/0459-1879-1999-4-1995-047

网格与高精度差分计算问题

PROBLEMS ABOUT GIRD AND HIGH ORDER SCHEMES

  • 摘要: 研究NS方程差分求解时来流雷诺数、计算格式精度和计算网格之间的关系.给出了判定空间三个方向上的粘性贡献在给定雷诺数、格式精度和网格下是否能够正确计入的估计方法.指出在NS方程的二阶差分方法的数值模拟中,由于物面法向采用了压缩网格技术,物面附近的网格间距很小,该方向上的粘性贡献可被计入.但是如果流向和周向的网格较粗,相应的差分方程中的粘性贡献可能落入截断误差相同的量级,因此在精度上等于仍是求解略去流向和周向粘性项的薄层近似方程.指出,高阶精度的差分计算格式,可以避免对网格要求苛刻的困难.并进一步讨论了建立高阶精度格式的问题,提出了建立高阶精度格式应该满足的原则:耗散控制原则以及色散控制原则.为了避免激波附近可能出现的微小非物理振荡,建议发展混合高阶精度格式,即在激波区,采用网格自适应的NND格式,在激波以外的区域,采用按上述原则发展的高阶格式.

     

    Abstract: In this paper, the relation between the difference scheme and grid system is studied for solving Navier-Stokes equations with given Reynolds number. Only if this relation is satisfied in the directions x, y, z respectively, the Navier-Stokes equations can be simulated properly. In many references solving full Navier-Stokes equations with second order difference scheme, the grids in the direction z normal to the wall airs fine enough since the clustering grid technique is used. The proposed relation is satis...

     

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