In this paper, numerical results which obtained by simulating moving shock discontinuity, contact discontinuity, uniform flow in curvilinear coordinate system and shock regular reflection are given, and the comparisons of the numerical results simulated by the first-order upwind scheme and the fifth-order WENO schemes are discussed. The shock and contact discontinuities simulated in the WENO schemes were found to exhibit more pronounced non-physical fluctuations and more complicated flow field structures during the change from the initial discontinuity to the numerical transition region than the results of the first-order upwind scheme. Also, the geometrically induced errors and boundary approximation model errors due to coordinate transformations are significantly larger than those of the first-order upwind scheme. Numerical and theoretical analysis of the phenomena above leads to the following conclusion in this paper: higher-order WENO schemes run the risk of magnifying errors in the results under certain computational conditions. Finally, inspired by recently published articles, this paper discusses the contradiction between the current spatial multi-point construction method in high-order schemes and the characteristic line theory of hyperbolic equations.
LIU Jun
,
HAN Fang
,
WEI Yan-Xin
. Discussions on the errors of high-order WENO schemes under some specific conditions[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 0
: 0
-0
.
DOI: 10.7527/S1000-6893.2020.24940
[1]刘君, 邹东阳, 徐春光.基于非结构动网格的非定常激波装配法[J].空气动力学学报, 2015, 33(1):10-16
[2]刘君, 邹东阳, 董海波.动态间断装配法模拟斜激波壁面反射[J].航空学报, 2016, 37(03):836-846
[3]ZOU D Y, XU CH G, DONG H B, L J.A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes[J].Journal of Computational Physics, 2017, 345:866-882
[4]CHANG S Y, BAI X Z, ZOU D Y, et al.An adaptive discontinuity fitting technique on unstructured dy-namic grids[J].Shock Waves, 2019, 29(8):1103-1115
[5]JIANG G, SHU C.Efficient Implementation of Weighted ENO Schemes[J].Journal of Computational Physics, 1996, 121(1):202-228
[6]HENRICK A, ASLAM T, POWERS J.Mapped Weighted Essentially Nonoscillatory Schemes: Achieving Optimal Order Near Critical Points[J].Journal of Computational Physics, 2005, 207(2):542-567
[7]BORGES R, CARMONA M, COSTA B, DON W.An Improved Weighted Essentially Non-oscillatory Scheme for Hyperbolic Conservation Laws[J].Journal of Computational Physics, 2008, 227(6):3191-3211
[8]Gottlieb S, Shu C-W.Total variation diminishing Runge–Kutta schemes[J].Math Comput, 1998, 67(221):73-85
[9]刘君, 韩芳.有关有限差分高精度格式两个应用问题的讨论[J].空气动力学学报, 2020, 38(2):244-253
[10]刘君, 魏雁昕, 韩芳.有限差分法的坐标变换诱导误差[J]. 航空学报:1-13 [2020-10-26]. http://kns.cnki.net/kcms/detail/11.1929.V.20201011.1620.012.html.
[11]NONOMURA T, TERAKADO D, ABE Y, FUJII K.A new technique for freestream preservation of finite-difference WENO on curvilinear grid[J].Computers & Fluids, 2015, 107:242-255
[12]ZHU Y J, SUN Z S, REN Y X, et al.A Numerical Strategy for Freestream Preservation of the High Or-der Weighted Essentially Non-oscillatory Schemes on Stationary Curvilinear Grids[J].Journal of scientific computing, 2017, 72(3):1021-1048
[13]朱志斌, 杨武兵, 禹旻.满足几何守恒律的格式及其应用[J].计算力学学报, 2017, 34(06):779-784
[14]DENG X G, MAO M L, TU G H, LIU H Y, ZHANG H X.Geometric conservation law and applications to high-order finite difference schemes with stationary grids[J].Journal of Computational Physics, 2011, 230:1100-1115
[15]刘君, 韩芳, 夏冰.有限差分法中几何守恒律的机理及算法[J].空气动力学学报, 2018, 36(6):917-926
[16]刘君, 韩芳.有限差分法中的贴体坐标变换[J].气体物理, 2018, 3(5):18-29
[17]SLOTNICK J P, KHODADOUST A, ALONSO J J, et al.CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences[R]. NASA CR-2014-218178, Langley Research Center, March 2014.
[18]DENG X, BOIVIN P, XIAO F.Revisit to the THINC scheme: A new formulation for two-wave Riemann solver accurate at contact interfaces[J].Physics of Fluids, 2019, 31(4):1-12
[19]钱战森.Godunov型显式大时间步长格式研究进展[J].航空学报, 2020, 41(07):87-115
[20]钱翼稷.空气动力学[M]. 北京: 北京航空航天大学出版社, 2011:201.
[21]童秉纲, 孔祥言, 邓国华.气体动力学[M]. 北京:高等教育出版社, 1990:232-237.
[22] MORETTI G.Thirty-six years of shock fitting[J].Computers & Fluids, 2002, 31:719-723
CJA