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人员 > 科研教学系列 > 吴开亮

吴开亮

副教授  

https://faculty.sustech.edu.cn/wukl

  • 简历
  • 科研
  • 教学
  • 发表论著

吴开亮,籍贯安徽省安庆市,理学博士,南方科技大学数学系和杰曼诺夫国际数学中心副教授、研究员、博士生导师。2011年获华中科技大学数学学士学位;2016年获北京大学计算数学博士学位;2016-2020年先后在美国犹他大学和美国俄亥俄州立大学从事博士后研究;2021年1月加入南方科技大学。研究方向包括微分方程数值解、机器学习与数据驱动建模、计算流体力学与数值相对论、高维逼近与不确定性量化等。研究成果发表在SIAM系列期刊SINUM/SISC (9篇)、J. Comput. Phys. (12篇)、M3AS、Numer. Math.、JSC、天体物理权威期刊ApJS、Phys. Rev. D等。曾获中国数学会计算数学分会 优秀青年论文奖一等奖(2015)和中国数学会 钟家庆数学奖(2019);入选国家青年人才计划、深圳市孔雀计划;主持国家自然科学基金面上项目。


研究领域

微分方程数值解、机器学习与数据科学、计算流体力学、计算物理、高维逼近论与不确定性量化


荣誉及获奖

◆ 2020:国家高层次人才计划(青年项目)

◆ 2019:中国数学会 钟家庆数学奖

◆ 2015:中国数学会计算数学分会 优秀青年论文奖一等奖

◆ 2014:北京大学 “挑战杯”五四青年科学奖一等奖


代表性论文 


◆ K. Wu

Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis,   56(4):2124--2147, 2018.


◆ K. Wu* and C.-W. Shu

Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes

Numerische Mathematik,   142(4): 995--1047, 2019.


◆ K. Wu and D. Xiu

Data-driven deep learning of partial differential equations in modal space

Journal of Computational Physics,   408: 109307, 2020. 


K. Wu and C.-W. Shu*
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
submitted for publication, 2021.  arXiv:2111.04722.  8 Nov 2021


◆ K. Wu* and C.-W. Shu

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Numerische Mathematik,   148: 699--741, 2021.


◆ K. Wu 

Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics

SIAM Journal on Scientific Computing,   43(6): B1164--B1197, 2021.


◆ Z. Sun, Y. Wei, and K. Wu*

On energy laws and stability of Runge--Kutta methods for linear seminegative problems

SIAM Journal on Numerical Analysis,   accepted for publication, 2022.


◆ K. Wu, H. Jiang, and C.-W. Shu
Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations
submitted to SIAM Journal on Numerical Analysis,   2022.


◆ K. Wu

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Physical Review D,   95, 103001, 2017. 


◆ Z. Chen, V. Churchill, K. Wu, and D. Xiu

Deep neural network modeling of unknown partial differential equations in nodal space

Journal of Computational Physics,     449: 110782, 2022.


◆ S. Cui, S. Ding, and K. Wu*
Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?
submitted to Journal of Computational Physics,   2022.


◆ K. Wu and Y. Xing

Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness

SIAM Journal on Scientific Computing,    43(1): A472--A510, 2021.


◆ Y. Chen and K. Wu*

A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes

Journal of Computational Physics,    466: 111398, 2022.


◆ H. Jiang, H. Tang, and K. Wu*

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

Journal of Computational Physics,     463: 111297, 2022.


◆ K. Wu, T. Qin, and D. Xiu

Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data

SIAM Journal on Scientific Computing,   42(6): A3704--A3729, 2020. 


◆ K. Wu and C.-W. Shu

Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations

SIAM Journal on Scientific Computing,   42(4): A2230--A2261, 2020. 


◆ Z. Chen, K. Wu, and D. Xiu

Methods to recover unknown processes in partial differential equations using data

Journal of Scientific Computing,   85:23, 2020. 


◆ K. Wu, D. Xiu, and X. Zhong

A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs 

Communications in Computational Physics,   30: 423--447, 2021.


◆ J. Hou, T. Qin, K. Wu and D. Xiu

A non-intrusive correction algorithm for classification problems with corrupted data

Commun. Appl. Math. Comput.3: 337--356, 2021.


◆ T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

Journal of Computational Physics,   395: 620--635, 2019.


◆ K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

Journal of Computational Physics,   384: 200--221, 2019.


◆ K. Wu and C.-W. Shu

A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics

SIAM Journal on Scientific Computing,   40(5):B1302--B1329, 2018.


◆ Y. Shin, K. Wu, and D. Xiu

Sequential function approximation with noisy data

Journal of Computational Physics,   371:363--381, 2018.


◆ K. Wu and D. Xiu

Sequential function approximation on arbitrarily distributed point sets

Journal of Computational Physics,   354:370--386, 2018.


◆ K. Wu and H. Tang

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

Z. Angew. Math. Phys.,   69:84(24pages), 2018.


◆ K. Wu, Y. Shin, and D. Xiu

A randomized tensor quadrature method for high dimensional polynomial approximation

SIAM Journal on Scientific Computing,   39(5):A1811--A1833, 2017. 


◆ K. Wu, H. Tang, and D. Xiu

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

Journal of Computational Physics,   345:224--244, 2017. 


◆ K. Wu and H. Tang

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

Math. Models Methods Appl. Sci. (M3AS),   27(10):1871--1928, 2017. 


◆ K. Wu and H. Tang

Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state

Astrophys. J. Suppl. Ser. (ApJS),   228(1):3(23pages), 2017. (2015 Impact Factor of ApJS: 11.257)


◆ K. Wu and H. Tang

A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics

SIAM Journal on Scientific Computing,   38(3):B458--B489, 2016. 


◆ K. Wu and H. Tang

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

Journal of Computational Physics,   298:539--564, 2015.


◆ K. Wu and H. Tang

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

Journal of Computational Physics,   256:277--307, 2014. 


◆ K. Wu, Z. Yang, and H. Tang

A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics

Journal of Computational Physics,   264:177--208, 2014. 


学术服务

◆ 美国《数学评论》评论员

◆ 期刊编委 Editorial Board of Numerical Analysis and Scientific Computation (specialty section of Frontiers in Applied Mathematics and Statistics)

◆ 下列期刊审稿人

  • Applied Numerical Mathematics
  • Chinese Journal of Theoretical and Applied Mechanics
  • Communications in Computational Physics
  • Computer Methods in Applied Mechanics and Engineering
  • Computers and Mathematics with Applications
  • East Asian Journal on Applied Mathematics
  • Electronic Research Archive
  • Engineering Optimization
  • Journal of Computational and Applied Mathematics
  • Journal of Computational Physics   ( > 50 times )
  • Journal of Numerical Mathematics
  • Journal of Scientific Computing
  • Journal of Applied Mathematics and Computing
  • Mathematical Models and Methods in Applied Sciences (M3AS)
  • Mathematica Numerica Sinica
  • SIAM Journal on Scientific Computing (SISC)
  • SIAM/ASA Journal on Uncertainty Quantification
  • Theoretical and Applied Mechanics Letters


招聘博士后和研究助理教授(RAP);每年计划招收博士生/硕士生 1-2名。

详情请见:https://faculty.sustech.edu.cn/?cat=11&tagid=wukl&orderby=date&iscss=1&snapid=1

有意者请将相关应聘或申请材料发送至:WUKL@sustech.edu.cn



保结构数值方法及其理论:保持正性、物理约束、平衡性、熵稳定、能量稳定/耗散、最小熵原理等结构

K. Wu, Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics, SIAM Journal on Numerical Analysis, 2018.

K. Wu and C.-W. Shu, Geometric quasilinearization framework for analysis and design of bound-preserving schemes, preprint, 2021.

K. Wu* and C.-W. Shu, Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes, Numerische Mathematik, 2019.

K. WuMinimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing,  2021.

K. Wu* and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, Numerische Mathematik, 2021.

K. Wu and H. TangAdmissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equationsMath. Models Methods Appl. Sci. (M3AS), 2017.

K. Wu and Y. Xing, Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness, SIAM Journal on Scientific Computing,  2021.

K. Wu and C.-W. Shu, Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations, SIAM Journal on Scientific Computing, 2020.

K. Wu and C.-W. Shu, A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics, SIAM Journal on Scientific Computing, 2018.

K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics, Physical Review D, 2017.

K. Wu and H. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.

H. Jiang, H. Tang, and K. Wu*, Positivity-preserving well-balanced central discontinuous Galekin schemes for the Euler equations under gravitational fields, Journal of Computational Physics, 2022.

Z. Sun, Y. Wei, and K. Wu*,  On energy laws and stability of Runge--Kutta methods for linear seminegative problems, SIAM Journal on Numerical Analysis, 2022.

K. Wu, H. Jiang, and C.-W. Shu, Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations, preprint, 2022.

S. Cui, S. Ding, and K. Wu*, Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?, preprint, 2022.


深度学习、数据驱动建模

K.Wu and D. Xiu, Data-driven deep learning of partial differential equations in modal space, Journal of Computational Physics, 2020.

T. Qin, K. Wu, and D. Xiu, Data driven governing equations approximation using deep neural networks, Journal of Computational Physics, 2019.

K.Wu, T. Qin, and D. Xiu, Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data, SIAM Journal on Scientific Computing, 2020.

Z. Chen, V. Churchill, K. Wu, and D. Xiu, Deep neural network modeling of unknown partial differential equations in nodal space, Journal of Computational Physics, 2022.

Z. Chen, K. Wu, and D. Xiu, Methods to recover unknown processes in partial differential equations using data, Journal of Scientific Computing, 2020.

J. Hou, T. Qin, K. Wu and D. Xiu,  A non-intrusive correction algorithm for classification problems with corrupted data, Commun. Appl. Math. Comput., 2020.

K. Wu and D. Xiu, Numerical aspects for approximating governing equations using data, Journal of Computational Physics, 2019.


相对论流体力学方程的数学性质与高阶精度数值方法

K. WuMinimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics, SIAM Journal on Scientific Computing,  2021.

K. Wu, Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics, Physical Review D, 2017.

K. Wu and H. Tang, High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics, Journal of Computational Physics, 2015.

K. Wu and H. Tang, Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations, Math. Models Methods Appl. Sci. (M3AS), 2017.

K. Wu* and C.-W. Shu, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, Numerische Mathematik, 2021.

K. Wu and H. Tang, A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2016.

K. Wu and H. Tang, Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state, Astrophys. J. Suppl. Ser. (ApJS), 2017.

K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics, Journal of Computational Physics, 2014.

Y. Chen and K. Wu*, A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes, Journal of Computational Physics, 2022.


高维函数逼近:大数据样本、最优采样、多项式逼近

K. Wu, Y. Shin, and D. XiuA randomized tensor quadrature method for high dimensional polynomial approximationSIAM Journal on Scientific Computing, 2017.

K. Wu and D. XiuSequential function approximation on arbitrarily distributed point setsJournal of Computational Physics, 2018.

Y. Shin, K. Wu, and D. Xiu, Sequential function approximation with noisy data, Journal of Computational Physics, 2018.

K. Wu and D. Xiu,  Sequential approximation of functions in Sobolev spaces using random samples, Commun. Appl. Math. Comput., 2019.


双曲守恒律方程的(广义)黎曼解Godunov型数值方法

K. Wu and H. Tang, A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics, SIAM Journal on Scientific Computing, 2016.

K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics, Journal of Computational Physics, 2014.

K. Wu, Z. Yang, and H. Tang, A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics, Journal of Computational Physics, 2014.


不确定性量化、随机Galerkin方法

K. Wu, D. Xiu, and X. Zhong, A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs, Communications in Computational Physics, 2021.

K. Wu, H. Tang, and D. Xiu, A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty, Journal of Computational Physics, 2017. 

Teaching(授课)

Fall Semester:Mathematical Experiments 数学实验(本科生)

Spring Semester:Computational Fluid Dynamics and Deep Learning 计算流体力学与深度学习(本研)

2021 Spring Semester:Calculus II 高等数学II(本科生)


Students & Postdocs(指导学生和博士后)

Postdoctoral Fellows
  ◆  Dr. Shengrong DING (2021.11-present):  Ph.D. from University of Science and Technology of China(中科大博士).  We have a joint article with Prof. Shumo Cui: "Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?" submitted to JCP.

  ◆  Dr. Junfeng CHEN (Visiting Postdoc Scholar;2022.03-present):  B.Sc. from Tsinghua University(清华本科),Ph.D. from Paris Sciences et Lettres – PSL Research University(法国巴黎文理研究大学博士). 

Graduate Students

  ◆  Haili JIANG (2021.04-2021.12),Visiting Ph.D. Student from Peking University(北京大学). 

  ◆  Fang YAN (2021.9-),Master Student,B.Sc. from South China University of Technology(华南理工).

  ◆  Zhuoyun LI (2022.09-),Ph.D. Student,B.Sc. from SUSTech(南科大).

  ◆  Manting PENG (2022.09-),Master Student,B.Sc. from SUSTech(南科大).

  ◆  Linfeng XU (2022.09-),Master Student,B.Sc. from SUSTech(南科大).

Undergraduate Students
  ◆  Xinran FANG 

  ◆  Yunhao JIANG:He was selected into a joint study program in University of Wisconsin-Madison.

  ◆  Zhuoyun LI:He will be a Ph.D. student in Sep. 2022.

  ◆  Zepei LIU:He will be a master student of Prof. Alexander KURGANOV in Sep. 2022. 

  ◆  Manting PENG:She will be a master student in Sep. 2022. 
  ◆  Mingrui WANG

  ◆  Yuanzhe WEI:  We have a joint article with Prof. Zheng Sun: "On energy laws and stability of Runge-Kutta methods for linear seminegative problems" accepted for publication in 《SIAM Journal on Numerical Analysis》(计算数学方向的顶级期刊,南科大本科生首次). He was selected to an exchange study program in MIT(麻省理工)南科大数学系第一位入选MIT交流项目的学生,见报道  https://mp.weixin.qq.com/s/nhlTvmGpdOrXuwZ-a7v4Tg 

  ◆  Linfeng XU:His major advisor was Prof. Yifei ZHU. He will be a master student in Sep. 2022. 

  ◆  Luowei YIN:He works on summer research and his bachelor thesis in our group (2021.04-2022.06) and will pursue his Ph.D. at CUHK(香港中文)in Sep. 2022. 


Welcome passionate and highly self-motivated students to join our group! If you are interested in our research, please feel free to contact me by email: WUKL@sustech.edu.cn.


招聘博士后和研究助理教授(RAP)。每年计划招收博士生/硕士生 1-2名。

详情请见:https://faculty.sustech.edu.cn/?cat=11&tagid=wukl&orderby=date&iscss=1&snapid=1

有意者请将相关应聘或申请材料发送至:WUKL@sustech.edu.cn


Publications List


[38] S. Cui, S. Ding, and K. Wu*
Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?
submitted for publication, 2022.


[37] K. Wu, H. Jiang, and C.-W. Shu

Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations
submitted for publication, 2022.


[36] Z. Sun, Y. Wei, and K. Wu*

On energy laws and stability of Runge--Kutta methods for linear seminegative problems

SIAM Journal on Numerical Analysis,  accepted for publication, 2022.


[35] K. Wu and C.-W. Shu*
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
submitted for publication, 2021.  arXiv:2111.04722.  8 Nov 2021


[34] K. Wu 
Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics

SIAM Journal on Scientific Computing,   43(6): B1164--B1197, 2021.


[33] Z. Chen, V. Churchill, K. Wu, and D. Xiu*
Deep neural network modeling of unknown partial differential equations in nodal space
Journal of Computational Physics,   449: 110782, 2022.


[32] K. Wu* and C.-W. Shu

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Numerische Mathematik,  148: 699--741, 2021.


[31] Y. Chen and K. Wu*
A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes
Journal of Computational Physics,   466: 111398, 2022.


[30] H. Jiang, H. Tang, and K. Wu*

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

Journal of Computational Physics,   463: 111297, 2022.


[29] K. Wu and Y. Xing

Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness

SIAM Journal on Scientific Computing,  43(1): A472--A510, 2021.


[28K. Wu and D. Xiu

Data-driven deep learning of partial differential equations in modal space

Journal of Computational Physics,  408: 109307, 2020. 


[27] K. Wu, T. Qin, and D. Xiu

Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data

SIAM Journal on Scientific Computing,  42(6): A3704--A3729, 2020. 


[26] K. Wu and C.-W. Shu

Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations

SIAM Journal on Scientific Computing,  42(4): A2230--A2261, 2020. 


[25] Z. Chen, K. Wu, and D. Xiu

Methods to recover unknown processes in partial differential equations using data

Journal of Scientific Computing,  85:23, 2020. 


[24] K. Wu, D. Xiu, and X. Zhong

A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs 

Communications in Computational Physics,  30: 423--447, 2021.


[23] J. Hou, T. Qin, K. Wu and D. Xiu

A non-intrusive correction algorithm for classification problems with corrupted data

Commun. Appl. Math. Comput., 3: 337--356, 2021.


[22] K. Wu* and C.-W. Shu

Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes

Numerische Mathematik,  142(4): 995--1047, 2019.


[21] T. Qin, K. Wu, and D. Xiu

Data driven governing equations approximation using deep neural networks

Journal of Computational Physics,  395: 620--635, 2019.


[20] K. Wu and D. Xiu

Numerical aspects for approximating governing equations using data

Journal of Computational Physics,  384: 200--221, 2019.


[19] K. Wu and D. Xiu

Sequential approximation of functions in Sobolev spaces using random samples
Commun. Appl. Math. Comput.,  1: 449--466, 2019.


[18] K. Wu and C.-W. Shu

A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics

SIAM Journal on Scientific Computing,  40(5):B1302--B1329, 2018.


[17] K. Wu

Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics
SIAM Journal on Numerical Analysis,  56(4):2124--2147, 2018.


[16] Y. Shin, K. Wu, and D. Xiu

Sequential function approximation with noisy data

Journal of Computational Physics,  371:363--381, 2018.


[15] K. Wu and D. Xiu

Sequential function approximation on arbitrarily distributed point sets

Journal of Computational Physics,  354:370--386, 2018.


[14] K. Wu and H. Tang

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

Z. Angew. Math. Phys.,  69:84(24pages), 2018.


[13] K. Wu and D. Xiu

An explicit neural network construction for piecewise constant function approximation

arXiv preprint arXiv:1808.07390, 2018.


[12] K. Wu, Y. Shin, and D. Xiu

A randomized tensor quadrature method for high dimensional polynomial approximation

SIAM Journal on Scientific Computing,  39(5):A1811--A1833, 2017. 


[11] K. Wu

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Physical Review D,  95, 103001, 2017. 


[10] K. Wu, H. Tang, and D. Xiu

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

Journal of Computational Physics,  345:224--244, 2017. 


[9] K. Wu and H. Tang

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

Math. Models Methods Appl. Sci. (M3AS),  27(10):1871--1928, 2017. 


[8] Y. Kuang, K. Wu, and H. Tang

Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid

Numer. Math. Theor. Meth. Appl.,  10(2):373--419, 2017. 


[7] K. Wu and H. Tang

Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state

Astrophys. J. Suppl. Ser. (ApJS),  228(1):3(23pages), 2017. (2015 Impact Factor of ApJS: 11.257)


[6] K. Wu and H. Tang

A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics

SIAM Journal on Scientific Computing,  38(3):B458--B489, 2016. 


[5] K. Wu and H. Tang

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Applied Mathematics and Mechanics,  37(11):1441--1466, 2016. 


[4] K. Wu and H. Tang

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

Journal of Computational Physics,  298:539--564, 2015.


[3] K. Wu, Z. Yang, and H. Tang

A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics

East Asian J. Appl. Math.,  4(2):95--131, 2014.


[2] K. Wu and H. Tang

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

Journal of Computational Physics,  256:277--307, 2014. 


[1] K. Wu, Z. Yang, and H. Tang

A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics

Journal of Computational Physics,  264:177--208, 2014.