显式类辛算法在双自转系外行星后牛顿轨道中的应用  

Application of an Explicit Symplectic-like Integrator in Post-Newtonian Orbits of Double-rotating Exoplanet System

作　　者：郑晶晶 王颖 刘福窑[1] 孙威 王雅茹 肖倩倩 陈奋 ZHENG Jing-jing;WANG Ying;LIU Fu-yao;SUN Wei;WANG Ya-ru;XIAO Qian-qian;CHEN Fen(Shanghai University of Engineering Science,School of Mathematics,Physics and Statistics,Shanghai 201620,China;Shanghai University of Engineering Science,Center of Application and Research of Computational Physics,Shanghai 201620,China)

机构地区：[1]上海工程技术大学数理与统计学院,上海201620 [2]上海工程技术大学计算物理与应用研究中心,上海201620

出　　处：《天文学进展》2022年第4期598-613,共16页Progress In Astronomy

基　　金：国家自然科学基金(11803020,U2031145,41807437);上海工程技术大学研究生科研创新项目(20KY2108)。

摘　　要：系外行星的长期动力学演化需要可靠的数值计算方法。辛算法具有保能量、保结构的特点,是研究哈密顿系统长期演化的最佳积分工具。双自转系外行星后牛顿哈密顿系统中坐标和动量不可分离,显式辛算法不能直接应用。利用相空间扩充构造显式类辛算法不会引入人工耗散,具有保能量的优势。主要探讨四阶中点置换相空间扩充显式类辛算法在双自转系外行星后牛顿轨道中的数值性能。结果表明,中点置换相空间扩充显式类辛算法,在顺行非近共面轨道的算法精度与RKF8(9)算法精度差一个量级;在逆行轨道和近圆轨道的算法精度与RKF8(9)算法精度相当;在偏心率小于0.9的轨道表现出高于同阶对比算法的算法精度。除此之外,该算法具有良好的稳定性,计算效率约是RKF8(9)的3倍。Long-term dynamical evolution of exoplanets requires reliable numerical computational methods.Symplectic algorithm has the advantage of conserving energy and structure,which is considered as the best integrator to simulate long-term evolution of Hamiltonian systems.Post-Newtonian Hamiltonian of double-rotating exoplanet system contains inseparable forms of coordinates and momenta,where explicit symplectic integrators cannot be applied directly.The use of phase space extension to construct the explicit symplectic-like algorithm does not introduce artificial dissipation and has the advantage of energy conservation.This paper mainly discusses the numerical performance of the fourthorder explicit extended phase space symplect-like method with midpoint permutations in post-Newtonian orbits of double-rotating exoplanet system.The results show that the accuracies of the fourth-order explicit extended phase space symplect-like method with midpoint permutations in prograde non near coplanar orbits are only one order of magnitude lower than that of RKF8(9),the accuracies of the algorithm in retrograde orbits and near circular orbits are equivalent to these of RKF8(9),and the accuracy of the algorithm in orbits with eccentricity less than 0.9 are higher than these of the same order comparison algorithms.In addition,the algorithm has good stability and the computational efficiency is about three times that of RKF8(9).

关 键 词：系外行星 隐式中点法 相空间扩充类辛算法 

分 类 号：P132[天文地球—天体力学]