Kun XU | Department of Mathematics

Kun XU

Kun XU
徐昆

BOOKS

$CFD Book$ Kun Xu, " A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes ", Elements in Aerospace Engineering, Cambridge University Press (2021)

$CFD Book$ Kun Xu, "Direct Modeling for Computational Fluid Dynamics construction and application of unified gas-kinetic schemes ", World Scientific (2015)

$CFD Book$ Wai-How Hui and Kun Xu, "Computational Fluid Dynamics Based on Unified Coordinates", Science Press (2012)

PREPRINTS

Xiaojian Yang, Kun Xu, "Wave–Particle Turbulent Simulation of Spatially Developing Round Jets Using a Non Equilibrium Transport Model with a Mixing Length Characteristic Time Closure". arXiv:2602.09759v1 [physics.flu-dyn] 10 Feb 2026

Yue Zhang, Xing Ji, Yibing Chen, Fengxiang Zhao, Kun Xu, "A single-stage high-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation". arXiv:2602.09482v1 [physics.comp-ph] 10 Feb 2026

Qihui Gao, Xing Ji, Zhifang Du, Shiyi Li, Yibing Chen, and Kun Xu, "The Stability Priority of Spatial-temporal Coupled Compact Element Methods overDecoupled Compact Element Methods". arXiv:2601.17264v1 [math-ph] 24 Jan 2026

Zhigang Pu, Wenpei Long, Kun Xu, "A Gas-Kinetic Scheme for Maxwell Equations". arXiv:2412.16845v2 [math.NA] 30 Dec 2025

Xiaozhe Xi, Junzhe Cao, Kun Xu, "The study of coherent Rayleigh-Brillouin scattering in multiple flow regimes using unified gas-kinetic scheme". arXiv:2512.15357v1 [physics.flu-dyn] 17 Dec 2025

Zhigang PU, Kun XU, "UGKS and UGKWP Methods for Multiscale Simulation of Electrostatic Plasma in Quasineutral and Hydrodynamic Limits". arXiv:2512.15406v1 [physics.comp-ph] 17 Dec 2025

Fengxiang Zhao, Jianping Gan, Kun Xu, "A Well-Balanced Space-Time ALE Compact Gas-Kinetic Scheme for the Shallow Water Equations on Unstructured Meshes". arXiv:2510.14673v1 [math.NA] 16 Oct 2025

Hongyu Liu, Xing Ji, Yuan Fu, Kun Xu, "A Geometric Multigrid-Accelerated Compact Gas-Kinetic Scheme for Fast Convergence in High-Speed Flows on GPUs". arXiv:2509.06347v1 [math.NA] 8 Sep 2025

Junlei Mu, Hong Zhang, Xing Ji, Yang Zhang, Gang Chen, Kun Xu, "Very High-order Compact Gas-kinetic Scheme With Discontinuity Feedback Factor". arXiv:2508.13705v1 [physics.comp-ph] 19 Aug 2025

Yue Zhang, Xing Ji, Kun Xu, "An implicit gas-kinetic scheme for internal and external flows". arXiv:2508.07644v1 [physics.flu-dyn] 11 Aug 2025

Zhigang Pu and Kun Xu, "Electromagnetic Flow Control in Hypersonic Rarefied Environment". arXiv:2507.14628v1 [physics.plasm-ph] 19 Jul 2025

Hongyu Liu, Xiaojian Yang, Chuang Zhang, Xing Ji, Kun Xu, "UGKWP and IUGKP methods for Multi-Scale Phonon Transport with Dispersion and Polarization". arXiv:2506.16203v1 [physics.comp-ph] 19 Jun 2025

Xiaojian Yang, Kun Xu, "Wave-Particle Based Multiscale Modeling and Simulation of Non-equilibrium Turbulent Flows". arXiv:2503.07207v1 [physics.comp-ph] 10 Mar 2025

Mingyu Quan, Kun Xu, "Kinetic model and numerical method for multispecies radiation hydrodynamic system with multiscale nonequilibrium transport". arXiv:2503.06906v1 [astro-ph.GA] 10 Mar 2025

Yixiao Wang, Xing Ji, Gang Chen, Kun Xu, "Comparison of the high-order Runge-Kutta discontinuous Galerkin method and gas-kinetic scheme for inviscid compressible flow simulations", arXiv:2404.19512v1 [math.NA] 30 Apr 2024

2026

Zhaoli Guo, Kun Xu, and Yajun Zhu, "A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales". Advances in Aerodynamics (2026) 8:8, https://doi.org/10.1186/s42774-025-00252-1

Hongyu Liu, Xiaojian Yang, Chuang Zhang, Xing Ji, Kun Xu, "Implicit unified gas kinetic particle method for steady-state solution of multiscale phonon transport". Acta Mech. Sin. 42, 325567 (2026), https://doi.org/10.1007/s10409-025-25567-x

Yaqing Yang, Fengxiang Zhao, Kun Xu, "An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows". Journal of Computational Physics 553 (2026) 114729. https://doi.org/10.1016/j.jcp.2026.114729

Yaqing Yang, Fengxiang Zhao, Kun Xu, "Performance evaluation of high-order compact and second-order gas-kinetic schemes in compressible flow simulations". arXiv:2508.19911v1 [math.NA] 27 Aug 2025. To appear in AIA.

Fengxiang Zhao, Kun Xu, A generalized ENO reconstruction in compact GKS for compressible flow simulations, Journal of Computational Physics 549 (2026) 114612, https://doi.org/10.1016/j.jcp.2025.114612

Jiawang Zhang, Xing Ji, Kun Xu, "Treatment of Wall Boundary Conditions in High-Order Compact Gas-Kinetic Schemes". Journal of Computational Physics 547 (2026) 114541.https://doi.org/10.1016/j.jcp.2025.114541.

Yufeng Wei, Junzhe Cao, Kun Xu, "Unified gas-kinetic scheme for reactive flow with multi-scale transport and chemical non-equilibrium". Journal of Computational Physics 546 (2026) 114514. https://doi.org/10.1016/j.jcp.2025.114514

Junzhe Cao, Yufeng Wei, Wenpei Long, Chengwen Zhong , Kun Xu, "Adaptive criterion and modification of wave-particle decomposition in UGKWP method for high-speed flow simulation". Computers and Fluids 305 (2026) 106896. https://doi.org/10.1016/j.compfluid.2025.106896

Gaocheng Liu, Fengxiang Zhao, Jianping Gan, Kun Xu, "A well-balanced gas-kinetic scheme with adaptive mesh refinement for shallow water equations". Ocean Engineering 343 (2026) 123298. https://doi.org/10.1016/j.oceaneng.2025.123298

2025

Hongyu Liu, Xing Ji, Yunpeng Mao, Zhe Qian, Kun Xu, "A Memory Reduction Compact Gas Kinetic Scheme on 3D Unstructured Meshes", Computer Physics Communications (2025), doi: https://doi.org/10.1016/j.cpc.2025.109981

Guiyu Cao, Liang Pan, Kun Xu and Shiyi Chen, "Double time‑relaxation kinetic model for compressible turbulence modeling", Advances in Aerodynamics (2025) 7:19. https://doi.org/10.1186/s42774-025-00230-7

Hongyu Liu, Xiaojian Yang, Chuang Zhang, Xing Ji, Kun Xu, "Unified gas-kinetic wave-particle method for multi-scale phonon transport", Physical Review E 112, 065304 (2025). DOI: 10.1103/hz9s-5qbm

Xiaojian Yang and Kun Xu, "Wave-Particle Turbulence Simulation of Spatially Developing Round Jets: Turbulent Flow Modeling and Method Validation". Phys. Fluids 37, 101706 (2025). doi: 10.1063/5.0293211

Zhaoli Guo, Yajun Zhu, and Kun Xu, "Kinetic representation of the unified gas-kinetic wave-particle method and beyond", to appear in Commun. Comput. Phys. doi: 10.4208/cicp.OA-2024-0192

Hongyu Liu, Xing Ji, Yunpeng Mao, Yuan Ding, Kun Xu, "A Compact Gas-Kinetic Scheme with Scalable ℎ𝑝 Multigrid Acceleration for Steady-State Computation on 3D Unstructured Meshes", Computer Physics Communications, 109820, doi: https://doi.org/10.1016/j.cpc.2025.109820.

Chengxiang Li, Xing Ji, Kun Xu, and Lian-Ping Wang, "The Effects of Spatial Reconstruction and Flux Solver on the Performance of High-Order Finite-Volume Compressible Flow Solvers", Commun. Comput. Phys. Vol. 38, No. 1, pp. 37-73 July 2025. doi: 10.4208/cicp.OA-2024-0180

Yue Zhang, Yufeng Wei, Wenpei Long, Kun Xu, "An efficiency and memory-saving programming paradigm for the unified gas-kinetic scheme", Computer Physics Communications 314 (2025) 109684, https:// doi.org/10.1016/j.cpc.2025.109684

Mingyu Quan, Xiaojian Yang, Yufeng Wei, Kun Xu, "Radiative hydrodynamic equations with nonequilibrium radiative transfer", PHYSICAL REVIEW D 111, 103038 (2025), DOI: 10.1103/PhysRevD.111.103038

Zhigang Pu and Kun Xu, "Unified Gas-Kinetic Wave-Particle Method for Multiscale Flow Simulation of Partially Ionized Plasma", Journal of Computational Physics 530 (2025) 113918, doi: https://doi.org/10.1016/j.jcp.2025.113918.

Xiaojian Yang, Yajun Zhu, Chang Liu, Kun Xu, "Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation", Journal of Computational Physics 522 (2025) 113587. https://doi.org/10.1016/j.jcp.2024.113587

Yaqing Yang, Liang Pan, Kun Xu, "Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes II: Unsteady flows", Journal of Computational Physics 521 (2025) 113534. doi: https://doi.org/10.1016/j.jcp.2024.113534.

2024

Wenpei Long, Yufeng Wei, Kun Xu, "An implicit adaptive unified gas-kinetic scheme for steady-state solutions of non-equilibrium flows", Phys. Fluids 36, 106114 (2024); doi: 10.1063/5.0232275

Guiyu Cao, Liang Pan, Kun Xu, Shiyi Chen, "High-Order Gas-Kinetic Scheme in General Curvilinear Coordinate for iLES of Compressible Wall-Bounded Turbulent Flows", Journal of Scientific Computing (2024) 101:35. https://doi.org/10.1007/s10915-024-02678-z

Hong Zhang, Xing Ji, Yue Zhao, Yuan Ding, Kun Xu, "A Robustness-Enhanced Reconstruction Based on Discontinuity Feedback Factor for High-Order Finite Volume Scheme", Journal of Scientific Computing (2024) 101:20. https://doi.org/10.1007/s10915-024-02655-6

Junzhe Cao, Sha Liu, Chengwen Zhong, Congshan Zhuo, Kun Xu, "Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation", Computers and Mathematics with Applications 174 (2024) 1–17. https://doi.org/10.1016/j.camwa.2024.08.017

Yufeng Wei, Wenpei Long, Kun Xu, "Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium", Computer Physics Communications 305 (2024) 109324. https://doi.org/10.1016/j.cpc.2024.109324

Yue Zhang and Kun Xu, "High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation", Journal of Computational Physics 515 (2024) 113270. doi: https://doi.org/10.1016/j.jcp.2024.113270.

Zhigang Pu, Chang Liu, Kun Xu, "Gas-Kinetic Scheme for Partially Ionized Plasma in Hydrodynamic Regime", Journal of Computational Physics 505 (2024) 112905. doi: https://doi.org/10.1016/j.jcp.2024.112905.

Yaqing Yang, Liang Pan, Kun Xu, "Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes I: Steady flows", Journal of Computational Physics 505 (2024) 112902. doi: https://doi.org/10.1016/j.jcp.2024.112902.

Xiaojian Yang, Wei Shyy, Kun Xu, "Unified gas-kinetic wave–particle method for polydisperse gas–solid particle multiphase flow", J. Fluid Mech. (2024), vol. 983, A37, doi:10.1017/jfm.2024.80.

Wenpei Long, Yufeng Wei, Kun Xu, "Nonequilibrium flow simulations using unified gas-kinetic wave-particle method", AIAAJ, Vol. 62, No. 4 (2024), pp. 1411-1433 doi: doi/abs/10.2514/1.J063641

Fengxiang Zhao, Jianping Gan, Kun Xu, "High-order Compact Gas-kinetic Scheme for Two-layer Shallow Water Equations on Unstructured Mesh", Journal of Computational Physics 498 (2024) 112651. https://doi.org/10.1016/j.jcp.2023.112651.

Yufeng Wei, Yajun Zhu, Kun Xu, "Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium", Journal of Computational Physics 497 (2024) 112610. doi: https://doi.org/10.1016/j.jcp.2023.112610.

Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu, "Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh", Journal of Computational Physics 497 (2024) 112590. doi: https://doi.org/10.1016/j.jcp.2023.112590.

2023

Chang Liu, Weiming Li, Yanli Wang, Peng Song, Kun Xu, "An implicit unified gas-kinetic wave-particle method for radiative transport process", Phys. Fluids 35, 112013 (2023); doi: 10.1063/5.0174774.

Yufeng Wei, Junzhe Cao, Xing Ji, Kun Xu, "Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations", Advances in Aerodynamics (2023) 5:25. https://doi.org/10.1186/s42774-023-00156-y.

Qing Xie, Xing Ji, Zihu Qiu, Chunlei Liang and Kun Xu, "High-Order Spectral Difference Gas-Kinetic Schemes for Euler and Navier-Stokes Equations", East Asian Journal on Applied Mathematics Vol. 13, No. 3, pp. 499-523. doi: 10.4208/eajam.2022-257.041222 August 2023.

Wenjin Zhao, Guiyu Cao, Jianchun Wang, Kun Xu, "High-order Gas-kinetic Schemes with Non-compact and Compact Reconstruction for Implicit Large Eddy Simulation", Computers and Fluids 256 (2023) 105846, doi: https://doi.org/10.1016/j.compfluid.2023.105846.

Yaqing Yang, Liang Pan, Kun Xu, "Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier–Stokes equations", Computers and Fluids 255 (2023) 105834, https://doi.org/10.1016/j.compfluid.2023.105834.

Yue Zhang, Xing Ji, Kun Xu, "A High-Order Compact Gas-Kinetic Scheme in a Rotating Coordinate Frame and on Sliding Mesh", INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 2023, VOL. 37, NO. 3, 181–200. https://doi.org/10.1080/10618562.2023.2178647

Zhaoli Guo, Jiequan Li , and Kun Xu, "Unified preserving properties of kinetic schemes", Physical Review E 107, 025301 (2023). DOI: 10.1103/PhysRevE.107.025301

Fengxiang Zhao, Xing Ji, Wei Shyy, Kun Xu, "Direct Modeling for Computational Fluid Dynamics and the Construction of High-order Compact Scheme for Compressible Flow Simulations", Journal of Computational Physics 477 (2023) 111921. https://doi.org/10.1016/j.jcp.2023.111921

Fengxiang Zhao, Xing Ji, Wei Shyy, Kun Xu, "High-order Compact Gas-kinetic Schemes for Three-dimensional Flow Simulation on Tetrahedral Mesh", Advances in Aerodynamics (2023) 5:1. https://doi.org/10.1186/s42774-022-00132-y.

Xiaojian Yang, Yufeng Wei, Wei Shyy, Kun Xu, "Unified gas-kinetic wave-particle method for three-dimensional simulation of gas-particle fluidized bed", Chemical Engineering Journal 453 (2023) 139541. https://doi.org/10.1016/j.cej.2022.139541

2022

Xing Ji, Wei Shyy, Kun Xu, "A p-multigrid compact gas-kinetic scheme for steady-state acceleration", Computers and Fluids 241 (2022) 105489.

Guiyu Cao, Yipeng Shi, Kun Xu, Shiyi Chen, "Modeling and simulation in supersonic three-temperature carbon dioxide turbulent channel flow", Phys. Fluids 34, 125121 (2022); https://doi.org/10.1063/5.0129353

Sha Liu, Kun Xu, and Chengwen Zhong, "Progress of the unified wave-particle methods for non-equilibrium flows from continuum to rarefied regimes", Acta Mech. Sin., Vol. 38, 122123 (2022), https://doi.org/10.1007/s10409-022-22123-x.

Xiaocong Xu, Yajun Zhu, Chang Liu, Kun Xu, "UGKS-based implicit iterative method for multiscale nonequilibrium flow simulations", SIAM J. SCI. COMPUT., Vol. 44 (2022), No. 4, pp. B996--B1017. https://doi.org/10.1137/21M1421398

Xiaojian Yang, Wei Shyy, Kun Xu, "Unified gas-kinetic wave-particle method for gas-particle two-phase flow from dilute to dense solid particle limit", Phys. Fluids 34, 023312 (2022); https://doi.org/10.1063/5.0081105.

Gyuha Lim, Yajun Zhu, and Kun Xu, "High-order Unified Gas-kinetic Scheme", Communications in Computational Physics, Vol. 32, No. 4, pp. 951-979, October 2022. doi: 10.4208/cicp.OA-2022-0113

Xiaojian Yang, Chang Liu, Xing Ji, Wei Shyy, Kun Xu, "Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow", Commun. Comput. Phys., Vol. 31, No. 3, pp. 669-706, March 2022. doi: 10.4208/cicp.OA-2021-0153

Fengxiang Zhao, Xing Ji, Wei Shyy, Kun Xu, "Compact high-order gas-kinetic scheme on unstructured mesh for acoustic and shock wave computations", Journal of Computational Physics 449 (2022) 110812, https://doi.org/10.1016/j.jcp.2021.110812.

Guiyu Cao, Liang Pan, Kun Xu, "High-order gas-kinetic scheme with parallel computation for direct numerical simulation of turbulent flows", Journal of Computational Physics 448(2022) 110739. https://doi.org/10.1016/j.jcp.2021.110739

Xiaojian Yang, Xing Ji, Wei Shyy, Kun Xu, "Comparison of the performance of high-order schemes based on the gas-kinetic and HLLC fl uxes", Journal of Computational Physics 448(2022) 110706. https://doi.org/10.1016/j.jcp.2021.110706

2021

Wenjin Zhao, Jianchun Wang, Guiyu Cao, "High-order gas-kinetic scheme for large eddy simulation of turbulent channel flows", Phys. Fluids 33, 125102 (2021); https://doi.org/10.1063/5.0071059.

Yajun Zhu, Kun Xu, "The first decade of unified gas kinetic scheme", arXiv:2102.01261v1 [physics.comp-ph] 2 Feb 2021.

Xing Ji, Wei Shyy, Kun Xu, "A Gradient Compression-Based Compact High-Order Gas-Kinetic Scheme on 3D Hybrid Unstructured Meshes", Int. J. Comput. Fluid Dyn., https://doi.org/10.1080/10618562.2021.1991329.

Yaqing Yang, Liang Pan, and Kun Xu, "High-order gas-kinetic scheme on threedimensional unstructured meshes for compressible flows", Phys. Fluids 33, 096102 (2021); https://doi.org/10.1063/5.0062368.

Yajun Zhu, Chengwen Zhong, and Kun Xu, "Numerical transport process of splitting kinetic schemes in the Navier-Stokes-Fourier limit", International Journal of Computational Fluid Dynamics,35:8 (2021), 653-665, DOI: 10.1080/10618562.2021.2023737.

Fengxiang Zhao, Jian-ping Gan, Kun Xu, "The study of shallow water flow with bottom topography by high-order compact gas-kinetic scheme on unstructured mesh", Phys. Fluids 33, 083613 (2021); doi: 10.1063/5.0060631.

Song Jiang, Kun Xu, Wenjun Sun, and Xiaojing Xu, "Unified gas kinetic schemes for the radiation transfer equations", SCIENTIA SINICA Mathematica, Vol. 51, No. 6 (2021), pp. 799-832 doi: 10.1360/SSM-2020-0278 (in Chinese)

Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu, "Compact High-Order Gas-Kinetic Scheme for Three-Dimensional Flow Simulations", AIAA J, Vol. 59, No. 8 (2021), pp. 2979-2996 doi: doi/abs/10.2514/1.J060208

Xiaocong Xu, Yipei Chen, Chang Liu, Zhihui Li, Kun Xu, "Unified gas-kinetic wave-particle methods V: diatomic molecular flow", Journal of Computational Physics 442(2021) 110496. https://doi.org/10.1016/j.jcp.2021.110496

Liang Pan and Kun Xu, "An Arbitrary-Lagrangian-Eulerian High-Order Gas-Kinetic Scheme for Three-Dimensional Computations", Journal of Scientific Computing (2021) 88:8. https://doi.org/10.1007/s10915-021-01525-9

Yajun Zhu, Chengwen Zhong, Kun Xu, "GKS and UGKS for High-Speed Flows", Aerospace 2021, 8, 141. https://doi.org/10.3390/aerospace8050141

Guiyu Cao, Liang Pan, Kun Xu, "Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence II: coarse-graining analysis of compressible Ksgs budget", Journal of Computational Physics 439 (2021) 110402.

Chang Liu and Kun Xu, "Unified Gas-kinetic Wave-Particle Methods IV: Multi-species Gas Mixture and Plasma Transport", Advances in Aerodynamics (2021) 3:9, https://doi.org/10.1186/s42774-021-00062-1

Cao GY, Pan L, Xu K, "High-order gas-kinetic scheme for numerical simulation of turbulence", Acta Aerodynamica Sinica, 2021. 39(1):168-176 doi:10.7638/kqdlxxb-2020.0156 (in CHINESE)

Liang Pan, Guiyu Cao, Kun Xu, "Fourth-order gas-kinetic scheme for turbulence simulation with multi-dimensional WENO reconstruction", Computers and Fluids 221 (2021) 104927; https://doi.org/10.1016/j.compfluid.2021.104927

Zhaoli Guo, Kun Xu, "Progress of discrete unified gas-kinetic scheme for multiscale flows", Advances in Aerodynamics (2021) 3:6; https://doi.org/10.1186/s42774-020-00058-3

Xiaocong Xu, Yipei Chen, Kun Xu, "Modeling and computation for non-equilibrium gas dynamics: beyond single relaxation time kinetic models", Phys. Fluids 33, 011703 (2021); https://doi.org/10.1063/5.0036203

2020

Wenjun Sun, Song Jiang, Kun Xu, Guiyu Cao, "Multiscale simulation for the system of radiation hydrodynamics", Journal of Scientific Computing (2020) 85:25. https://doi.org/10.1007/s10915-020-01337-3

Fengxiang Zhao, Xing Ji, Wei Shyy, and Kun Xu (2020), "An acoustic and shock wave capturing compact high-order gas-kinetic scheme with spectral-like resolution", International Journal of Computational Fluid Dynamics, https://doi.org/10.1080/10618562.2020.1821879

Yipei Chen, Yajun Zhu, Kun Xu, "A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes", Phys. Fluids 32, 096108 (2020); https://doi.org/10.1063/5.0021199

Chang Liu and Kun Xu, "A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation", Advances in Aerodynamics (2020) 2:21. https://doi.org/10.1186/s42774-020-00045-8

L. Pan and K. Xu, "High-order gas-kinetic scheme in curvilinear coordinates for the Euler and Navier-Stokes solutions", Commun. Comput. Phys. Vol. 28, No. 4, pp. 1321-1351 (2020). doi: 10.4208/cicp.OA-2019-0141

Yajun Zhu, Chengwen Zhong, Kun Xu, "Ray Effect in Rarefied Flow Simulation", Journal of Computational Physics 422(2020) 109751. https://doi.org/10.1016/j.jcp.2020.109751

Shuang Tan, Wenjun Sun, Kun Xu, Junxia Wei, and Guoxi Ni, "Time implicit unified gas kinetic scheme for 3D multi-group neutron transport simulation", Commun. Comput. Phys. Vol. 28, No. 3, pp. 1189-1218 (2020). doi: 10.4208/cicp.OA-2019-0050

Xing Ji, Kun Xu, "Performance Enhancement for High-order Gas-kinetic Scheme Based on WENO-adaptive-order Reconstruction", Commun. Comput. Phys., Vol. 28, No. 2, pp. 539-590, doi: 10.4208/cicp.OA-2019-0082, August 2020.

Tianbai Xiao, Chang Liu, Kun Xu, Qingdong Cai,"A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows", Journal of Computational Physics 415(2020) 109535, doi: https://doi.org/10.1016/j.jcp.2020.109535.

Liang Pan, Fengxiang Zhao, Kun Xu, "High-order ALE gas-kinetic scheme with WENO reconstruction", Journal of Computational Physics 417(2020) 109558, doi: https://doi.org/10.1016/j.jcp.2020.109558.

LIU Chang, XU Kun, "Direct modeling methodology and applications in multiscale transport process", ACTA Aerodynamica Sinica, Vol. 38, No. 2, April 2020 (In CHINESE).

Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu, "A HWENO Reconstruction Based High-order Compact Gas-kinetic Scheme on Unstructured Mesh", Journal of Computational Physics 410 (2020) 109367.

Songze Chen, Zhaoli Guo, and Kun Xu, "A well-balanced gas kinetic scheme for Navier-Stokes equations with gravitational potential", Commun. Comput. Phys. Vol. 28, No. 3, pp. 902-926 (2020). doi: 10.4208/cicp.OA-2019-0067

Weiming Li, Chang Liu, Yajun Zhu, Jiwei Zhang, Kun Xu, "Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport", Journal of Computational Physics 408 (2020) 109280.

Liang Pan, Kun Xu, "High-order gas-kinetic scheme with three-dimensional WENO reconstruction for the Euler and Navier-Stokes solutions", Computers and Fluids 198 (2020) 104401.

Chang Liu, Yajun Zhu, and K. Xu, "Unified Gas-kinetic Wave-Particle methods I: Continuum and Rarefied Gas Flow ", Journal of Computational Physics 401 (2020) 108977.

2019

Chang Liu, Guangzhao Zhou, Wei Shyy, Kun Xu, "Limitation Principle for Computational Fluid Dynamics", Shock Waves (2019) 29:1083-1102. https://doi.org/10.1007/s00193-018-0881-6

Guiyu Cao, Liang Pan, Kun Xu, "Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: criterion for direct numerical simulation", Computers and Fluids 192 (2019) 104273.

Mohammad Afzal Shadaba, Dinshaw Balsarab, Wei Shyy, and Kun Xu, "Fifth order finite volume WENO in general orthogonally-curvilinear coordinates", Computers and Fluids 190 (2019) 398-424.

Guiyu Cao, Hongmin Su, Jinxiu Xu, Kun Xu, "Implicit High-Order Gas Kinetic Scheme for Turbulence Simulation", Aerospace Science and Technology 92 (2019) 958-971.

Yajun Zhu, Chang Liu, Chengwen Zhong, Kun Xu, "Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh", Phys. Fluids 31, 067105 (2019). https://doi.org/10.1063/1.5097645.

Fengxiang Zhao, Xing Ji, Wei Shyy, Kun Xu, "Compact Higher-order Gas-kinetic Schemes with Spectral-like Resolution for Compressible Flow Simulations", Advances in Aerodynamics (2019) 1:13. https://doi.org/10.1186/s42774-019-0015-6.

Yajun Zhu, Chengwen Zhong, Kun Xu, "An Implicit Unified Gas-kinetic Scheme for Unsteady Flow in All Knudsen Regimes", Journal of Computational Physics 386 (2019) 190-217.

T.B. Xiao, K.Xu, and Q.D. Cai, "A unified gas-kinetic scheme for multiscale and multicomponent flow transport", Appl. Math. Mech. -Engl. Ed., 40(3), 355-372 (2019). https://doi.org/10.1007/s10483-019-2446-9

Chang Liu, Zhao Wang, Kun Xu, "A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows VI: Dilute Disperse Gas-Particle Multiphase System", Journal of Computational Physics 386 (2019) 264-295.

Wenjun Sun, Song Jiang, Kun Xu, "Multiscale Radiative Transfer in Cylindrical Coordinates", Communications on Applied Mathematics and Computation (2019) 1:117-139. https://doi.org/10.1007/s42967-019-0007-x

2018

G.Y. Cao, H.L. Liu, and K. Xu,"Physical Modeling and Numerical Studies of Three-dimensional Non-equilibrium Multi-temperature Flows", Physics of Fluids 30, 126104 (2018); doi: 10.1063/1.5065455.

Liang Pan, Kun Xu, "Two-Stage Fourth-order Gas-kinetic Scheme for Three-dimensional Euler and Navier-Stokes Solutions", Int. J. Comput. Fluid Dynamics 32 (2018) 395-411.

Xing Ji, Liang Pan, Wei Shyy, Kun Xu, "A Compact Fourth-order Gas-kinetic Scheme for the Euler and Navier-Stokes Solutions", Journal of Computational Physics 372 (2018) 446-472.

T.B. Xiao, K.Xu, Q.D. Cai, and T.Z. Qian "An investigation of non-equilibrium heat transport in a gas system under external force field", International Journal of Heat and Mass Transfer 126 (2018) 362-379.

Shiyi Li, Qibing Li, Song Fu, Kun Xu, "A Unified Gas-Kinetic Scheme for Axisymmetric Flow in all Knudsen Number Regimes", Journal of Computational Physics 366 (2018), pp.144-169.

X. Ji, F.X. Zhao, W. Shyy, and K. Xu, "A Family of High-order Gas-kinetic Schemes and Its Comparison with Riemann Solver Based High-order Methods", Journal of Computational Physics 356 (2018), pp. 150-173.

Guangzhao Zhou, Kun Xu, and Feng Liu, "Grid-converged Solution and Analysis of the Unsteady Viscous Flow in a Two-dimensional Shock Tube", Physics of Fluids 30, 016102 (2018)

Wenjun Sun, Song Jiang, Kun Xu, "An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-dependent Radiative Tansfer Equations", Int. J. of Numerical Analysis and Modeling, Volume 15, Number 1-2, Pages 134-153 (2018).

Li-jun Xuan, Kun Xu, "An efficient high-order finite difference gas-kinetic scheme for the Euler and Navier-Stokes equations", Computers and Fluids, Volume 166, Pages 243-252 (2018).

2017

W.J. Sun, S. Jiang, and K. Xu, "A Multidimensional Unified Gas-kinetic Scheme for Radiative Transfer Equations on Unstructured Mesh", Journal of Computational Physics 351 (2017), pp. 455-472.

Y.J. Zhu, Chongwen Zhong, and K. Xu,"Unified Gas-kinetic Scheme with Multigrid Convergence for Rarefied Flow Study", Physics of Fluids 29, 096102 (2017); doi: 10.1063/1.4994020

C. Wang, H. Yan, Q.B. Li, and K. Xu,"Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes", Journal of Computational Physics 350 (2017), pp. 237-259.

C. Liu and K. Xu,"A Unified Gas Kinetic Scheme for Continuum and Rarefied Flows V: Multiscale and Multi-component Plasma Transport", Commun. Comput. Phys., Vol. 22, No. 5, pp. 1175-1223, November 2017 (doi: 10.4208/cicp.OA-2017-0102).

Xiaodong Ren, Kun Xu, and Wei Shyy, "A gas-kinetic theory based multidimensional high-order method for the compressible Navier-Stokes solutions", Acta Mech. Sin. (2017) 33(4): 733-741.

Wei Xu, Liang Pan, Bo Gao, Yi Chiu, Kun Xu and Yi-Kuen Lee, "Systematic study of packaging designs on the performance of CMOS thermoresistive micro calorimetric flow sensors", J. Micromech. Microeng. 27 (2017) 085001 (10pp).

Lei Wu, Minh Tuan Ho, Lefki Germanou, Xiao-Jun Gu, Chang Liu, Kun Xu and Yonghao Zhang, "On the apparent permeability of porous media in rarefied gas flows", J. Fluid Mech. (2017), vol. 822, pp. 398-417.

W.J. Sun, S. Jiang, and K. Xu, "An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits", Commun. Comput. Phys., Vol. 22 (2017), No. 4, pp. 889-912, October.

L. Pan, J.Q. Li, and K. Xu,"A Few Benchmark Test Cases for Higher-order Euler Solvers", Numer. Math. Theor. Meth. Appl., Vol. 10, No. 4, pp. 711-736, November (2017).

Liang Pan, Junxia Cheng, Shuanghu Wang, Kun Xu, "A two-stage fourth-order gas-kinetic scheme for compressible multicomponent flows", Commun. Comput. Phys., Vol. 22 (2017), No. 4, pp. 1123-1149, October.

Guangzhao Zhou, Kun Xu, Feng Liu, "Simplification of the flux function for a high-order gas-kinetic evolution model", Journal of Computational Physics 339 (2017), pp. 146-162.

K.Xu and C. Liu,"A Paradigm for Modeling and Computation of Gas Dynamics", Physics of Fluids 29, 026101 (2017).

2016

S.Z. Chen, K. Xu, and Z.H. Li,"Cartesian grid method for gas kinetic scheme on irregular geometries", Journal of Computational Physics 326 (2016), 862-877.

L. Pan, K. Xu, Q.B. Li, and J.Q. 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.

R.J. Wang, X.P. Xu, K. Xu, and T.Z. Qian, "Onsager's Cross Coupling Effects in Gas Flows Confined to Micro-channels", Physical Review Fluids 1, 044102 (2016).

S.Z. Chen, Z.L. Guo, and K. Xu, "Simplification of the unified gas kinetic scheme", Physical Review E 94, 023313 (2016).

Z.L. Guo and K. Xu,"Discrete unified gas kinetic scheme for multiscale heat transfer based on the phonon Boltzmann transport equation", International Journal of Heat and Mass Transfer 102 (2016), 944-958.

L. Pan and K. Xu,"A Third-order Compact Gas-kinetic Scheme on Unstructured Meshes for Compressible Navier-Stokes Solutions", J. Comput. Phys. 318 (2016), 327-348.

Xiaodong Ren, Kun Xu, and Wei Shyy, "A multi-dimensional high-order DG-ALE method based on gas-kinetic theory with application to oscillating airfoils", J. Comput. Phys. 316 (2016), 700-720.

Yajun Zhu, Chengwen Zhong, and Kun Xu, "Implicit unified gas-kinetic scheme for steady state solution in all flow regimes", J. Comput. Phys. 315 (2016), pp. 16-38.

Chang Liu, Kun Xu, Quanhua Sun, and Qingdong Cai "A unified gas-kinetic scheme for continuum and rarefied flow IV: full Boltzmann and model equations", J. Comput. Phys. 314 (2016), 305-340.

Lianhua Zhu, Zhaoli Guo, and Kun Xu,"Discrete unified gas kinetic scheme on unstructured meshes", Computers and Fluids 127 (2016) 211-225 .

2015

L. Pan and K. Xu,"A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations", Commun. Comput. Phys., Vol. 18 (2015), No. 4, pp. 985-1011.

Wenjun Sun, Song Jiang, Kun Xu, and Shu Li, "An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer system", J. Comput. Phys. Vol. 302 (2015), pp. 222-238.

L. Pan and K. Xu,"A third-order gas-kinetic scheme for three-dimensional inviscid and viscous flow computations", Computers & Fluids 119 (2015) 250-260.

Kun Xu,"Direct modeling for computational fluid dynamics", Acta Mech Sin (2015), 31(3), pp. 303-318.

Zhaoli Guo, Ruijie Wang, and Kun Xu,"Discrete unified gas kinetic schemes for all Knudsen number flows: II. compressible case", Phy. Rev. E. 91, 033313 (2015).

X.D. Ren, K. Xu, W. Shyy and C.W. Gu,"A Multi-dimensional High-order Discontinuous Galerkin Method Based on Gas Kinetic Theory for Viscous Flow Computations", J. Comput. Phys. Vol. 292 (2015), pp. 176-193.

Peng Wang, Lianhua Zhu, Zhaoli Guo, and Kun Xu,"A comparative study of LBE and DUGKS methods for nearly incompressible flows", Commun. Comput. Phys.Vol. 17 (2015), No.3, pp. 657-681.

Songze Chen, Kun Xu, and Qingdong Cai "A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models". Advances in Applied Mathematics and Mechanics. 7 (2015), pp. 245-266.

Songze Chen and Kun Xu, "A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit", J. Comput. Phys. Vol. 288 (2015), pp. 52-65.

L. Pan, K. Xu, Generalized Coordinate Transformation and Gas-kinetic Scheme, J. Comput. Phys. Vol. 287 (2015), pp. 207-225.

Kun Xu and Songze Chen, Gas-kinetic scheme in hypersonic flow simulation (in CHINESE), Acta Aeronautica et Astronautica Sinica, Vol. 36 (2015), pp. 135-146. Special Issue on Hypersonic Flows.

Wenjun Sun, Song Jiang, and Kun Xu "An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations", J. Comput. Phys. Vol. 285 (2015), pp. 265-279.

2014

Xu K, Li Q B, Li Z W. Direct modeling-based computational fluid dynamics (in Chinese). Sci Sin-Phys Mech Astron, 2014, 44: 519-530, doi: 10.1360/SSPMA2013-00054

Ruijie Wang, Kun Xu, "Unified gas-kinetic simulation of slider air bearing", Theoretical and Applied Mechanics Letters, Vol. 4, 022001 (2014).

S. Liu, P.B. Yu, K. Xu, and Z.W. Zhong, "Unified Gas Kinetic Scheme for Diatomic Molecular Simulations in All Flow Regimes", Journal of Computational Physics, 259 (2014), pp. 96-113.

2013

Zhaoli Guo, Kun Xu, Ruijie Wang, "Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case", Physical Review E 88, 033305 (2013).

J. Luo and K. Xu, "A high-order multidimensional gas-kinetic scheme for hydrodynamic equations", Science China, Technological Sciences, Vol. 56, No. 10, pp. 2370-2384, October 2013.

T. Ohwada, R. Adachi, K. Xu, J. Luo,"On the remedy against shock anomalies in kinetic schemes", J. Comput. Phys. 255 (2013), 106-129.

M. Fossati, A. Guardone, L. Vigevano, and K. Xu, "Kinetic node-pair formulation for two-dimensional flows from continuum to transition regime", AIAA Journal, Vol. 51, No. 4, pp. 784-796, April 2013.

J.C. Huang, K. Xu, and P.B. Yu, "A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations", Commun. Comput. Phys., vol. 14, No. 5, pp. 1147-1173, November, 2013.

J. Luo, L.J. Xuan, and K. Xu, "Comparison of fifth-order WENO scheme and WENO-gas-kinetic scheme for inviscid and viscous flow simulation", Commun. Comput. Phys., Vol. 14, No. 3, pp. 599-620, September, 2013.

L.J. Xuan and K. Xu, "A new gas-kinetic scheme based on analytical solutions of the BGK equation" Journal of Computational Physics, vol. 234 (2013), 524-539.

2012

K. Xu, "Unified treatment of rarefied and continuum fluid flows", in Encyclopedia of Aerospace Engineering, eds R. Blockley and W. Shyy, John Wiley: Chichester. DOI: 10.1002/9780470686652.eae601. Published 17th December 2012.

S.Z. Chen, K. Xu, and C.B. Lee "The dynamic mechanism of a moving Crookes radiometer", Physics of Fluids, 24, 111701 (2012).

S.Z. Chen, K. Xu, C.B. Li, and Q.D. Cai, "A Unified Gas Kinetic Scheme with Moving Mesh and Velocity Space Adaptation", J. Comput. Phys.. 231, Issue 20, pp. 6643-6664, August (2012).

H.W. Liu, K. Xu, T.S. Zhu, W.J. Ye, "Multiple temperature kinetic model and its applications to micro-scale gas flows", Computers and Fluids, vol. 67, pp. 115-122, July (2012).

Q.B. Li and K. Xu, "Progress in Gas-kinetic Scheme" (Review Paper in Chinese), Advances in Mechanics, vol. 42, no. 5, pp. 522-537, September (2012).

R.J. Wang and K. Xu, "The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme", Acta Mechanica Sinica, vol. 28(4), pp. 1022-1029 (2012).

J.C. Huang, K. Xu, and P.B. Yu, "A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows II: Multi-dimensional Cases", Communications in Computational Physics, vol. 12, No. 3, pp. 662-690, September (2012).

2011

K. Xu and Z. Guo, "Multiple temperature gas dynamic equations for non-equilibrium flows", J. Comput. Math, Vol. 29, No. 6, pp. 639-660, 2011.

J. Luo, K. Xu, and N. Liu, "A well-balanced symplecticity-preserving gas-kinetic scheme for hydrodynamic equations under gravitational field", SIAM J. Sci. Comput. Vol. 33, No. 5, pp. 2356-2381, 2011.

Jiequan Li, Qibing Li, Kun Xu, "Comparison of the Generalized Riemann Solver and the Gas-Kinetic Scheme for Inviscid Compressible Flow Simulations", Journal of Computational Physics, vol. 230 (2011), pp. 5080-5099.

K. Xu and J.C. Huang, "An improved unified gas-kinetic scheme and the study of shock structures", IMA J. of Applied Mathematics, vol. 76,No. 5, pp. 698-711, October (2011).

K. Xu, Q.H. Sun, and P.B. Yu, "Valid physical processes from numerical discontinuities in computational fluid dynamics", Int. J. of Hypersonics, Vol. 1, No. 3, pp. 157-171, September (2011).

2010

H.W. Liu, K. Xu, T.S. Zhu, and W.J. Ye, "A multiple temperature kinetic model and its application to micro-scale gas flow simulations", conference paper for 13th Asian congress of fluid mechanics, 17-21 December 2010, Dhaka, Bangladesh.

C. Jin, K. Xu, and S.Z. Chen, "A three dimensional gas-kinetic scheme with moving mesh for low-speed viscous flow computation", Adv. Appl. Math. Mech., vol. 2, no. 6, 746-762, December, 2010.

H.Z. Tang, K. Xu, and C.P. Cai, "Gas-kinetic scheme for three dimensional magnetohydrodynamics", Numer. Math. Theor. Meth. Appl., Vol. 3, No. 4, 387-404, November 2010.

K. Xu and J.C. Huang, "A unified gas-kinetic scheme for continuum and rarefied flows", J. Comput. Physics, vol. 229 (2010), pp. 7747-7764 (October).

Q.B. Li, K. Xu, and S. Fu, "A high-order gas-kinetic Navier-Stokes flow solver", J. Comput. Phys. 229 (2010), pp. 6715-6731 (September).

Typos in this paper

K. Xu, J. Luo, and S.Z. Chen, "A well-balanced kinetic scheme for gas dynamic equations under gravitational field", Advances in Applied Mathematics and Mechanics, vol. 2, no. 2, 200-210, April, 2010.

2009

E. Josyula, K. Xu, C.J. Suchyta III, and W.F. Bailey, "Kinetic methods for solving the internal structure of shock waves", 41st AIAA Thermophysics Conference, 22-25 June 2009, San Antonio, Texas.

K. Xu and Z. Guo, "Generalized gas dynamic equations with multiple translational temperatures", Modern Physics Letter B, vol. 23 (2009), pp. 237-240.

G. Ni, S. Jiang, and K. Xu, "Remapping-free ALE-type kinetic method for flow computations", J. Comput. Phys., vol. 228 (2009), pp. 3154-3171.

H. Luo, L. Luo, and K. Xu, "A Discontinuous Galerkin method based on BGK scheme for the Navier-Stokes equations on arbitrary grids", Advances in Applied Mathematics and Mechanics, vol. 1 (2009), pp. 301-318.

Z.L. Guo and K. Xu, "Numerical validation of Brenner's hydrodynamic model by force driven Poiseuille flow", Advances in Applied Mathematics and Mechanics, vol. 1 (2009), pp. 391-401.

Z.L. Guo and K. Xu, "Generalized Gas Dynamic Equations", 47th AIAA Aerospace Sciences Meeting, AIAA 2009-672 (2009).

2008

K. Xu, H.W. Liu, "A Multiple temperature kinetic model and its application to near continuum flows", Commun. Comput. Phys., vol. 4 (2008), No. 5, pp. 1069-1085.

K. Xu, X. He, C. Cai, "Multiple temperature kinetic model and gas-kinetic method for hypersonic nonequilibrium flow computations", J. Comput. Phys., vol. 227 (2008), pp. 6779-6794.

K. Xu, "A generalized Bhatnagar-Gross-Krook model for nonequilibrium flows", Physics of Fluids, vol. 20, 026101 (2008).

G.X. Ni, S. Jiang, K. Xu, "A DGBGK scheme based on WENO limiters for viscous and inviscid flows", J. Comput. Phys., vol. 227 (2008), pp. 5799-5815.

Z.L. Guo, H.W. Liu, L.S. Luo, K. Xu, "A comparative study of the LBM and GKS methods for 2D near incompressible flows", J. Comput. Phys., vol. 227 (2008), pp. 4955-4976.

C.P. Cai, D. Liu, K. Xu, "A one-dimensional multiple-temperature gas-kinetic BGK scheme for shock wave computation", AIAA J.(American Institute of Aeronautics and Astronautics), vol. 46 (2008), No. 5, pp. 1054-1062.

Guoxi Ni, Song Jiang, K. Xu, "Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes", J. Comput. Phys., vol. 227, pp.3015-3031 (2008).

W. Liao, Y. Peng, L.S. Luo, K. Xu, "Modified gas-kinetic scheme for shock structures in argon", Progress in Computational Fluid Dynamics, vol. 8, pp. 97-108 (2008).

C.Q. Jin, K. Xu, "Numerical study of the unsteady aerodynamics of freely falling plates", Communications in Computational Physics, vol. 3, pp. 834-851 (2008).

2007

J.Y. Yang, T.Y. Hsieh, Y.H. Shi, K. Xu, "High order kinetic flux vector splitting schemes in general coordinates for ideal quantum gas dynamics", J. Comput. Phys., vol. 227, pp. 967-982, December (2007)

W. Liao, L.S. Luo, K. Xu, "Gas-kinetic scheme for continuum and near-continuum hypersonic flows", J. Spacecraft and Rockets, vol. 44, No. 6, pp. 1232-1240, Nobember-December (2007)

C.L. Tian, K. Xu, K.L. Chan, and L.C. Deng, "A three-dimensional multidimensional gas kinetic scheme for the Navier-Stokes equations under gravitational fields", J. Comput. Phys., vol. 226, pp. 2003-2027 (2007).

K. Xu and H. Liu, "Multiscale gas-kinetic simulation for continuum and near continuum flows", Physical Review E, E75, 016306 (2007).

K. Xu, H. Liu, and J. Jiang "Multiple temperature kinetic model for continuum and near continuum flows", Physics of Fluids, vol. 19, 016101 (2007).

Hongwei Liu and K. Xu "A Runge-Kutta Discontinuous Galerkin Method for Viscous Flow Equations", J. Comput. Phys. 224 (2007), pp. 1223-1242.

Changqiu Jin and K. Xu, "A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation", J. Comput. Phys. 222 (2007), pp. 155-175.

2006

C.H. Pan and K. Xu, "KFVS scheme for shallow water equations on unstructured mesh", Journal of Hydraulics (CHINESE), vol. 37, No. 7, pp. 858-864 (2006).

K. Xu and E. Josyula, "Continuum formulation for non-equilibrium shock structure calculation", Communications in Computational Physics, vol. 1, No. 3, pp. 425-450 (2006).

K. Xu and E. Josyula, "Gas-kinetic scheme for rarefied flow simulation", Mathematics and Computers in Simulation 72(2006), pp.253-256. (Discrete Simulation of Fluid Dynamics in Complex Systems)

M. Torrilhon and K. Xu, "Stability and consistency of kinetic upwinding for advection-diffusion equations", IMA Journal of Numerical Analysis, vol. 26, pp.686-722 (2006).

M.S. Ghidaoui, A.A. Kolyshkin, J.H. Liang, F.C. Chan, Q. Li, and K. Xu, "Linear and nonlinear analysis of shallow wakes", J. Fluid Mech. vol. 548 (2006), pp. 309-340.

Changqiu Jin and K. Xu, "An adaptive grid method for two dimensional viscous flows", J. Comput. Phys. vol. 218, pp.68-81 (2006).

Y.T. Que and K. Xu, "The study of roll-waves in inclined open channels and solitary wave run-up", Int. J. Numer. Methods in Fluids, vol. 50, pp. 1003-1027 (2006).

2005

M.L. Mao, K. Xu, and X.G. Deng, "The application of gas-kinetic BGK scheme in near continuum flow regime", Acta Aerodynamica Sinica (CHINESE), Vol. 23, No. 3, 317-321 (2005).

Q.B. Li, S. Fu, and K. Xu, "Application of BGK scheme with kinetic boundary conditions in hypersonic flow", AIAA J.(American Institute of Aeronautics and Astronautics), vol. 43, pp. 2170 (2005).

K. Xu and E. Josyula, "A multiple translational temperature model and its shock structure solution", Physical Review E 71, 056308 (2005).

Q. Li, S. Fu, and K. Xu, "A compressible Navier-Stokes flow solver with scalar transport", J. Comput. Phys., vol. 204 (2005), pp. 692-714.

K. Xu, M.L. Mao, and L. Tang, "A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow", J. Comput. Phys., vol. 203 (2005), pp. 405-421.

2004

T. Ohwada and K. Xu, "The kinetic scheme for full Burnett equations", J. Comput. Phys., vol. 201 (2004), pp.315-332.

K. Xu, "Discontinuous Galerkin BGK method for viscous flow equations: one-dimensional systems", SIAM J. on Scientific Computing, Vol. 23, No. 6, pp. 1941-1963 (2004).

K. Xu and Z.H. Li, "Microchannel flows in slip flow regime: BGK-Burnett solutions", J. Fluid Mechanics (2004), vol. 513, pp. 87-110

K. Xu and L. Tang, "Non-equilibrium BGK model for nitrogen shock structure", Phys. of Fluids 16 (2004), pp. 3824.

2003

K. Xu and X.Y. He, "Lattice Boltzmann method and Gas-kinetic BGK scheme in the low Mach number viscous flow simulations", J. Comput. Phys., Vol. 190, pp. 100-117 (2003).

K. Xu, "Super-Burnett solutions for Poiseuille flow", Physics of Fluids, Vol. 15, No. 7, pp. 2077-2080 (2003).

2002

K. Xu, "A well-balanced gas-kinteic scheme for the shallow water equations with source terms", J. Comput. Phys. Vol. 178 (2002), pp. 533-562.

K. Xu, "Regularization of the Chapman-Enskog expansion and its description of shock structure", Physics of Fluids, Vol.14, No.4, pp. L17-L20 (2002).

K. Xu, "A Slope-update Scheme for Compressible Flow Simulation", J. Comput. Phys. Vol. 178 (2002), pp. 252-259. (Central point: importance of time accuracy for a CFD code)

2001

H.Z. Tang, K. Xu, and P. Cheng, "Numerical simulation of resonant oscillations in a tube", Numerical Heat Transfer, Part A, 40:37-54 (2001).

S. Lui and K. Xu, "Entropy Analysis of KFVS Schemes for the compressible Euler Equations", Z. angew. Math. Phys., Vol. 52 (2001), pp. 62-78. (central point: gases in different cells are initially distinguishable. The entropy definition for a mixture is different from a single component gas).

K. Xu and Z.W. Li, "Dissipative Mechanism in Godunov-type Schemes", Int. J. Numer. Methods in Fluids, Vol. 37, pp. 1-22 (2001).

K. Xu, "A Gas-kinetic BGK Scheme for the Navier-Stokes Equations, and Its Connection with Artificial Dissipation and Godunov Method", J. Comput. Phys., Vol. 171 (2001), pp. 289-335.

Typos in the paper

Comment on "Development of an Improved Gas-kinetic BGK Scheme for Inviscid and Viscous Flows" [J. Comput. Phys., 158, 1-27 (2000)] (JCP Vol. 171, pp. 843-847 (2001) )

H.Z.. Tang and K.Xu, "Pseudoparticle Representation and Positivity Analysis of Explicit and Implicit Steger-Warming FVS Schemes", Z. angew. Math. Phys. 52 (2001) 847-858.

K.Xu, "A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Flow",J. of Comput. Physics 166 (2001), No. 2, pp. 383-399.

J.Q. Deng, M.S. Ghidaoui, W.G. Gray, and K. Xu, "A Boltzmann-based Mesoscopic Model for Contaminant Transport in Flow System", Advances in Water Resources 24 (2001), pp. 531-550.

Selected Publications before 2001

K. Xu, "Gas-Kinetic Schemes for Unsteady Compressible Flow Simulations" (VKI report 1998-03 (1998))

H.Z. Tang and K. Xu, "A High-order Gas-kinetic Method for Multidimensional Ideal Magnetohydrodynamics", J. Comput. Phys. 165 (2000), pp. 69-88.

K. Xu, "Gas-kinetic Theory based Flux Splitting Method for Ideal MHD Equations", J. Comput. Phys. 153 (1999), pp. 334-352.

K. Xu, "Gas-kinetic Schemes for Fluid Simulations" (invited lecture at 1st International Conference on Computational Fluid Dynamics, July 9 - July 14, 2000, Kyoto, Japan.)

Y.S. Lian and K. Xu, "A Gas-kinetic Schemes for Multimaterial Flows and Its Application in Chemical Reactions", J. Comput. Phys., Vol. 163, pp. 349-375 (2000).

Y.S. Lian and K. Xu, "A Gas-kinetic Scheme for Reactive Flows", Computers and Fluids, Vol. 29 (2000), pp. 725-748.

K. Xu and S.H. Lui, "Rayleigh-Bernard simulation using the gas-kinetic Bhatnagar-Gross-Krook scheme in the incompressible limit", Phy. Rev. E Vol. 60 (1999), pp. 464-470.

T. Tang and K. Xu, "Gas-kinetic schemes for the compressible Euler equations: positivity-preserving analysis", Z. angew. Math. Phys. Vol. 50 (1999), pp. 258-281.

M. Su, K. Xu, and M.S. Ghidaoui, "Low-speed flow simulation by gas-kinetic scheme", J. Comput. Phys., Vol. 150, pp. 17-39 (1999).

K. Xu and J. Hu, "Projection dynamics in Godunov-type schemes", J. Comput. Phys., Vol. 142, pp. 412-427 (1998).

K. Xu and L.S. Luo, "Connection between Lattice Boltzmann Equation and Beam Scheme", Int. J. of Modern Physics C 9, No. 8, pp. 1177-1188 (1998).

K. Xu, "BGK-based scheme for multicomponent flow calculations", J. Comput. Phys., Vol. 134, pp. 122-133 (1997).

K. Xu, C. Kim, L. Martinelli, and A. Jameson, "BGK-based scheme for the Simulation of Compressible Flow", International Journal of Computational Fluid Dynamics, Vol. 7, No. 3, pp. 213 (1996).

K. Xu, "A New Class of Gas-Kinetic Relaxation Schemes for the Compressible Euler Equations", J. of Stat. Phys. 81, pp. 147-164 (1995).

K. Xu, L. Martinelli, and A. Jameson, "Gas-kinetic finite volume methods, flux-vector splitting, and artificial diffusion", J. Comput. Phys., Vol. 120, pp. 48-65 (1995).

K. Xu and K. Prendergast, "Numerical Navier-Stokes solutions from gas-kinetic theory", J. Comput. Phys., Vol. 114, pp. 9-17 (1994).

K.Prendergast and K. Xu,"Numerical hydrodynamics from gas-kinetic theory", J. Comput. Phys., Vol. 109, pp. 53-66 (1993).

PhD Thesis (1993)

part 1

part 2

part 3

part 4