研究人员
顾问
北大客座教授
中心成员

 

李杰权

 

北京应用物理与计算数学研究所研究员

大变形流体力学团队首席 

联系方式:
联系电话:010-61935465
电子邮箱:li_jiequan@iapcm.ac.cn
个人主页:http://math0.bnu.edu.cn/~lijiequan

 

教育经历:

1997年获中国科学院数学研究所博士学位

1994年获北京师范大学数学系硕士学位

 

工作经历:

(一年以上长期职位)

2015/08---:北京应用物理与计算数学研究所高级特聘研究员,博士生导师

2010/12—2015/07:北京师范大学数学科学学院教授、博士生导师

2013/07—2014/06:美国宾州州立大学数学系,访问教授

2002/08—2010/12:北京市首都师范大学数学科学学院研究员(2003 年始博士生导师)

2004/03—2005/06: 德国马格德堡大学数学系,洪堡学者

2001/08—2002/07:台北中央研究院数学所访问教授

1999/10—2001/08:以色列希伯莱大学爱因斯坦数学所Lady Davis和Golda Meir Fellow(以色列总理基金资助)

1997/03—1998/12:中国科学院应用数学所博士后

 

研究领域:


计算流体力学

数值分析

偏微分方程

计算流体力学

 

背景资料:

· 计算流体力学:

面向航天航空、武器物理以及其它工程应用领域,致力发展三高(高置信度、高精度、高效)数值方法。涉及的背景问题有:可压缩流体的普适性问题、爆轰、弹塑性材料、信号传输、多介质流体的界面不稳定性等。感兴趣的问题有: 可压缩流体力学的高精度数值方法,包括有限体积、有限差分、间断有限元方法等; 从介观到宏观的多介质流体力学数学建模; 可压缩湍流的形成机理以及大规模数值模拟; 团队成员与美国、德国、瑞士、法国、意大利、以色列、日本、香港等国家和地区有着密切的合作关系。每两年有定期的多介质流体力学国际会议以及每年有小规模的高精度数值方法国际会议,推动着该领域内同行的合作与交流。

· 数值分析

数值分析是理解、评价数值方法的重要手段,也是设计高置信度数值方法的基础。本方向致力于:分析各种新型数值方法的稳定性; 针对复杂物理模型,分析相应数值方法保物理性质;

· 偏微分方程
基于无粘欧拉方程组和 BGK 模型,研究可压缩流体的流场结构及其各种非线性波(激波、滑移面、爆轰波、Delta 波等)的稳定性。具体有: 可压缩欧拉方程组的两维黎曼问题以及多维非线性波的相互作用; 从稀薄到连续流相关模型的适定性。美国数学会Mathematical Reviews评价其所在团队的成果为“中国数学学派”(Chinese School of Mathematics)的工作。

 

所获奖项:

国务院政府特殊津贴(2008)

教育部新世纪优秀人才(2006)

第十届霍英东高等学校青年教师奖(研究类, 2005)

德国洪堡研究类奖学金(2004)

北京市科学技术一等奖(2003,排名第一)

以色列 Golda Meir(总理)奖(2001,2002)


科研项目:

1. 国家自然科学基金面上项目(主持),11771054,可压缩多介质流体力学的广义黎曼问题数值方法,2018/01-2021/01。

2. 国家自然科学基金面上项目, 真正多维时空高精度黎曼解法器及其应用,2014/01-2017/12,已结题,主持。

3. 教育部博士点基金(主持):基于移动网格的广义黎曼问题格式,2014/01—2016/12(基金号:20130003110004) 。

3.北京师范大学自主创新重点项目(主持):几类流体力学方程组数学理论,2013--2015 (基金号:2012LZD08)。

4.国家自然科学基金重点项目(参加): 非线性双曲型和混合型偏微分方程,2011/01—2014/12 (基金号:11031001)。

5.国家自然科学基金重大研究计划(参加):多介质大变形流体的真正多维高保真算法,2012/01—2014/12(基金号91130021)。

6. 国家自然科学基金(主持): 多维可压缩欧拉方程的自相似解,2010/01--2012/12 (基金号:10971142)。

7. 北京市自然科学基金项目和北京市教育委员会科技发展计划重点项目(主持): 计算流体力学中的有限体积格式,2009/01--2011/12(基金号:KZ200910028002)。

8. 北京市拔尖创新人才项目:2005-2007年, 2009年-2011年。

9. 973子项目: 流体力学与材料科学中的偏微分方程(成员),2007/01—2010/12(基金号:2006CB805902)

10. 教育部新世纪优秀人才项目:2006-2008年。

11. 北京市自然科学基金项目和北京市教育委员会科技发展计划重点项目(主持): 流体力学及其相关问题,2005/01—2007/12。

12.人事部留学人员科技活动择优资助项目(独立):气体动力学中的高维非线性波的数值研究, 2004/04—2007/04。

13. 第九届霍英东高等院校青年教师研究类基金:气体动力学中非线性波的结构和大时间稳定性,2004/03—2007/3。

14.北京市自然科学基金(主持): 气体动力学中的有限体积格式和高维非线性波的数值研究,2004/01—2006/12。

15.国家自然科学青年基金(独立):高维非线性守恒律组解的结构和高精度守恒性差分格式,2004/01—2006/12。

16.北京市组织部基金(独立):流体力学中的相关问题,2003/01—2005/12。

17.国家教育部归国留学人员启动基金(独立),2003年:非线性双曲守恒律。

18.解放军总装备部国防重点实验室项目(参加):爆燃波向爆轰波的转化,2000/01--2004/12。

19.国家自然科学基金(参加): 非线性守恒律的二维黎曼问题,1998/01—2000/12。

20.中国教育部博士后基金(独立):高维非线性守恒律的差分格式和数值模拟, 1997/01—1998/12。

 

专著:

The Two-dimensional Riemann Problem in Gas Dynamics (第一作者;合作者:Tong Zhang, Shuli Yang), Pitmann Monographs and Surveys in Pure and Applied Mathematics 98, 312页, Longman Scientific & Technical, Harlow.

(美国数学会数学评论MR1697999 (2000d:76106):More recently, the two-dimensional Riemann problem has attracted the attention of many researchers, particularly the Chinese school of mathematics: J. Li, D. Tan, S. Yang, T. Zhang, Y. Zheng, etc . A complete and rigorous study is presented for both the two-dimensional scalar conservation laws and the zero-pressure gas dynamics model. Many important properties of the structure and qualitative behavior of solutions are derived for the two-dimensional compressible Euler system. Precise conjectures are stated, which are carefully tested in numerical experiments.)

代表论文:

[1] Xin Lei and Jiequan Li, A non-oscillatory energy-splitting method for the computation of compressible multi-fluid flows, Physics of Fluids, 30 (2018), 006891.

[2] Zhifang Du and Jiequan Li, A Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws, Journal of Computational Physics, 355 (2018), 385-396.

[3] Zhifang Du and Jiequan Li, A two-stage fourth order time-accurate discretization for   Lax-Wendroff type flow solvers, II. High order numerical boundary conditions 369(2018), 125-147.

[4] Dinshaw Balsara, Jiequan Li and Gino I. Montecinos, An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver, Journal of Computational Physics, in (minor) revision, 2018.

[5] Jiequan Li and Yue Wang, Thermodynamical effects and high resolution methods for compressible fluid flows, Journal of Computational Physics, 343 (2017), 340–354.

[6] Jiequan Li, Baolin Tian and Shuanghu Wang, Dissipation Matrix and Artificial Heat Conduction for Godunov-type Schemes  of  Compressible Fluid Flows, International Journal of Numerical Methods in Fluids, 84 (2017), 57-75.

[7] Liang Pan, Kun Xu, Qibing Li and Jiequan Li, An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations, Journal of Computational Physics, 326 (2016), 197-221.

[8] Jiequan Li and Zhifang Du, A two-stage  fourth order time-accurate discretization for  Lax-Wendroff type flow solvers, I. Hyperbolic conservation laws, SIAM J. Sci. Comput.. 38 (2016), 3045-3069.  

[9] Yue Wang and Jiequan Li, Numerical Defects of the HLL Scheme and Dissipation Matrices for the Euler equations, SIAM J. Numerical Analysis, No. 52, Vol. 1(2014), 207-219.

[10] Jianzhen Qian, Jiequan Li and Shuanghua Wang, The generalized Riemann problems for compressible fluid flows: Towards high order, Journal of Computational Physics, 259 (2014) 358–389.  

[11] Jiequan Li and Yongjin Zhang, The adaptive GRP scheme for compressible fluid flows over unstructured meshes, Journal of Computational Physics, 242 (2013), 367--386.

[12] Jiequan Li and Zhicheng Yang, Heuristic modified equation analysis on oscillations in numerical solutions of conservation laws, SIAM Journal on Numerical Analysis, 49 (2001), 2386-2406.

[13] Jiequan Li, Qibing Li and Kun Xu, Comparison of the Generalized Riemann Solver and the Gas-Kinetic scheme for Compressible Inviscid Flow Simulations, Journal of Computational Physics, 230 (2001), 5080-5099.

[14] Jiequan Li and Yuxi Zheng, Interaction of four rarefaction waves in the bi-symmetric class of the two-dimensional Euler equations, Communications in Mathematical Physics, 296 (2010), 303--321.

[15] Ee Han, Jiequan Li and Huazhong Tang, An adaptive GRP scheme for compressible fluid flows, Journal of Computational Physics, 229 (2010), 1448-1466.

[16] Jiequan Li and Yuxi Zheng, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Archive Rational Mechanics and Analysis, 193 (2009), 623--657.

[17] Jiequan Li, Huazhong Tang, Gerald Warnecke and Lumei Zhang, Local oscillations in finite difference solutions of hyperbolic conservation laws, Mathematics of Computation, 78 (2009), 1997--2018.

[18] Jiequan Li, Tiegang Liu and Zhongfeng Sun, Implementation of the GRP scheme for computing spherical compressible fluid flows, Journal of Computational Physics, 228 (2009), 5867--5887.

[19] J. Glimm, X. Ji, Jiequan Li, X. Li, T. Zhang, P. Zhang and Y. Zheng, Transonic shock formation in a rarefaction Riemann problem for the 2-D compressible Euler equations, SIAM Journal on Applied Mathematics, 69 (2008), 720--742.

[20] Jiequan Li and Zhongfeng Sun, Remark on the generalized Riemann problem method for compressible fluid flows, Journal of Computational Physics, 222 (2007), 796--808.

[21] M.Ben-Artzi and Jiequan Li, Hyperbolic conservation laws: Riemann invariants and the generalized Riemann problem, Numerische Mathematik, 106 (2007), 369--425.

[22] Jiequan Li and Guoxian Chen, The generalized Riemann problem method for the shallow water equations with bottom topography, International Journal of Numerical Methods in Engineering, 65 (2006), 834--862.

[23] Matania Ben-Artzi, Jiequan Li and Gerald Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, Journal of Computational Physics, 218 (2006), 19--43.

[24] Jiequan Li, Tong Zhang and Yuxi Zheng, Simple waves and a characteristic decomposition for the two dimensional compressible Euler equations, Communications in Mathematical Physics, 267 (2006), 1--12.

[25] Jiequan Li and Peng Zhang, The transition from ZND to CJ theories for nonconvex scalar combustion model, SIAM Journal on Mathematical Analysis, 34 (2003), 675--699.

[26] Jiequan Li, Global solution of an initial—value problem for two--dimensional compressible Euler equations, Journal of Differential Equations, 179 (2002), 178-- 194.

[27] Jiequan Li, On the two--dimensional gas expansion for compressible Euler equations, SIAM Journal on Applied Mathematics, 62 (2001/2002), 831--852.

[28] Jiequan Li, On the uniqueness and existence problem for a multidimensional reacting and convection system, Journal of the London Mathematical Society, 62 (2000), 473-- 488.

 

其他期刊部分论文:

[1] Jin Qi, Baolin Tian and Jiequan Li, A high-order cell-centered Lagrangian method with a vorticity-based adaptive nodal solver for 2-D compressible Euler equations, Communications in Computational Physics, 24 (2018), 774-790.

[2] Rui Chen, Jiequan Li and Baolin Tian, Application of  the GRP Scheme for  two-dimensional cylindrical compressible fluid flows, Communications in Computational Physics, accepted, 2017.  

[3] Liang Pan, Jiequan Li and Kun Xu, A Few Benchmark Test Cases for Higher-order Euler Solvers, Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), 489-514.

[4] Jin Qi and Jiequan Li, A fully discrete high order ALE method over untwisted time-space control volumes, International Journal of Numerical Methods in Fluids, 83 (2017), 625-641.

[5] Yue Wang and Jiequan Li, Entropy Convergence of a New Two-Value Scheme with Slope Relaxation for Conservation Laws, Applied Mathematics and Mechanics, 37 (2016), 1151-1170.

[6] Jiequan Li, Self-similar solutions of 2-D compressible Euler equations and mixed-type problems, Bulletin of the Institute of Mathematics, Academia Sinica, 10 (2015), 393--421.

[7] Jin Qi, Yue Wang and Jiequan Li, Remapping-free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations, Communications in Computational Physics, 15(2014), 1029-1044.

[8] Yanbo Hu, Jiequan Li and Wancheng Sheng, Degenerate Goursat-type boundary value problems arising from the study of two-dimensional isothermal Euler equations, Z. Angew. Math. Phys.,63 (2012), 1021-1046.

[9] Jiequan Li, Zhicheng Yang and Yuxi Zheng, Characteristic decompositions and interactions of rarefaction waves of 2-D Euler Equations, Journal of Differential Equations, 250 (2011), 782–798, 2011.

[10] Ee Han, Jiequan Li and Huazhong Tang, Accuracy of the adaptive GRP scheme and the simulation of 2-D Riemann problem for compressible Euler equations, Communications in Computational Physics, 10 (2011), 577-606.

[11] Matania Ben-Artzi,Joseph Falcovitz and Jiequan Li, The convergence of the GRP scheme, Discrete and Continuous Dynamical Systems, 23 (2009) 1--27.

[12] Jiequan Li, Wancheng Sheng, Tong Zhang and Yuxi Zheng, Two-dimensional Riemann problems: From scalar conservation laws to compressible Euler equations, Acta Mathematica Scientia, 29 (2009), 777--802.

[13] M. Ben-Artzi, J. Falcovitz and Jiequan Li, Wave interaction and numerical approximation for two-dimensional scalar conservation laws, Computational Fluid Dynamics Journal, 14 (2006), 401-418.

[14] Jiequan Li and Gerald Warnecke, Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics, Advances in Differential Equations, 8 (2003), 961--1004.

[15] Jiequan Li, Maria Lukacova-Medvidova and Gerald Warnecke, Evolution Galerkin schemes applied to the two-dimensional Riamann problem for the wave equation system, Discrete and Continuous Dynamical Systems, 9 (2003), 559--573.

[16] Shaozhong Chen, Jiequan Li and Tong Zhang, Transition from a deflagration to a detonation in gas dynamic combustion, Chinese Annals of Mathematics 24B (2003), 423-432.

[17] Jiequan Li and Wei Li, The Riemann problem for zero-pressure flow in gas dynamics, Progresses in Natural Sciences, 11 (2001), 331--344.

[18] Jiequan Li, Note on the compressible Euler equations with zero temperature, Applied Mathematical Letter, 14 (2001), 519--523.

[19] Jiequan Li and Hanchun Yang, Delta-shocks as limit of solutions of multidimensional zero-pressure gas dynamics, Quarterly of Applied Mathematics, 59 (2001), 315--342.

[20] Jiequan Li and Shuli Yang, Two-dimensional Riemann problem for Euler equations of gas dynamics in three pieces, Journal of Computational Mathematics, 17 (1999), 327--336.

[21] Peng Zhang, Jiequan Li and Tong Zhang, On Two-dimensional Riemann problem for pressure-gradient equations in gas dynamics, Discrete and Continuous Dynamical Systems, 4 (1998), 609--634.

[22] Shaozhong Cheng, Jiequan Li and Tong Zhang, Explicit construction of measure solutions of Cauchy problem for transportation equations, Science in China (Series A), 40 (1997),1287--1299.


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Tel: 86-10-62753944      E-mail: jyxii@pku.edu.cn; ganqiumei@pku.edu.cn