Book: WaiHow Hui and Kun Xu, "Computational Fluid Dynamics Based on Unified Coordinates", Science Press (2012)
DISCUSSION AREA
Here is the principle about the best physical result a numerical scheme can provide under the cell resolution.
You are welcome to try these test cases if you have confidence on your higherorder schemes for the Euler equations.
CFD can go beyond numerical PDE. Traditional concepts of stability, consistency, and convergence need to be upgraded.
An Alternative Analysis of Discontinuous Galerkin Method and Possible Directions for Developing Higherorder Schemes
Thoughts on computational fluid dynamics by Hong Xiao (in CHINESE)
Anyone working on Lattice Boltzmann Methods may be interested in the following papers about Discrete Unified Gaskinetic Scheme (DUGKS).
 Phy. Rev. E 88, 033305 (2013).
 (Phy. Rev. E. 91, 033313 (2015)).
 Comparison among LBGK, MRT, and DUGKS in the regime where the Lattice Boltzmann Method is applicable.
Discussion on Moment and DVM (in CHINESE) (23/1/2014).
 Equivalence between Moment and DVM by LI Ruo et al .
 Comment on Equivalence
 Direct Modeling for CFD (English)
PREPRINTS
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu, "A HWENO Reconstruction Based Highorder Compact Gaskinetic
Scheme on Unstructured Meshes", preprint, 13 September, 2018.
Chang Liu, Guangzhao Zhou, Wei Shyy, Kun Xu, "Limitation Principle for Computational Fluid Dynamics",
26 May 2018.
Tianbai Xiao, Kun Xu, Qingdong Cai,"A velocityspace adaptive unified gas kinetic scheme for continuum
and rarefied fl
ows", ArXiv:1802.04972v1[physics.compph] 14 Feb. 2018.
Chang Liu, Zhao Wang, Kun Xu, "A Unified Gaskinetic Scheme for Continuum and Rarefied Flows VI:
Dilute Disperse GasParticle Multiphase System", ArXiv:1802.04961v2[physics.compph], revised manuscript, 11 Sept. 2018.
Wenjun Sun, Song Jiang, Kun Xu, "Multiscale Radiative Transfer in Cylindrical Coordinates", preprint, Jan 2018.
Yajun Zhu, Chengwen Zhong, Kun Xu, "An Implicit Unified Gaskinetic Scheme for Unsteady Flow in All
Knudsen Regimes", preprint, Jan 2018.
Liang Pan, Kun Xu, "TwoStage Fourthorder Gaskinetic Scheme for Threedimensional
Euler and NavierStokes Solutions", arXiv:1801.08870v1[math.NA] 25 Jan 2018.
Mohammad Afzal Shadaba, Dinshaw Balsarab, Wei Shyy, and Kun Xu, "Fifth order finite volume WENO in general
orthogonallycurvilinear coordinates", arXiv:1711.06212v1 [physics.compph], 16 Nov 2017.
2018
Xing Ji, Liang Pan, Wei Shyy, Kun Xu, "A Compact Fourthorder Gaskinetic Scheme for the Euler and
NavierStokes Solutions", Journal of Computational Physics 372 (2018) 446472.
T.B. Xiao, K.Xu, Q.D. Cai, and T.Z. Qian "An investigation of nonequilibrium heat transport in a gas
system under external force field", International Journal of Heat and Mass Transfer 126 (2018) 362379.
Shiyi Li, Qibing Li, Song Fu, Kun Xu, "A Unified GasKinetic Scheme for Axisymmetric Flow in all
Knudsen Number Regimes", Journal of Computational Physics 366 (2018), pp.144169.
X. Ji, F.X. Zhao, W. Shyy, and K. Xu, "A Family of Highorder Gaskinetic Schemes
and Its Comparison with Riemann Solver Based Highorder Methods",
Journal of Computational Physics 356 (2018), pp. 150173.
Guangzhao Zhou, Kun Xu, and Feng Liu, "Gridconverged Solution and Analysis of the
Unsteady Viscous Flow in a Twodimensional Shock Tube",
Physics of Fluids 30, 016102 (2018)
Wenjun Sun, Song Jiang, Kun Xu, "An Asymptotic Preserving Implicit Unified Gas
Kinetic Scheme for Frequencydependent Radiative Tansfer Equations", Int. J. of Numerical Analysis and Modeling,
Volume 15, Number 12, Pages 134153 (2018).
Lijun Xuan, Kun Xu, "An efficient highorder finite difference gaskinetic scheme
for the Euler and NavierStokes equations", Computers and Fluids,
Volume 166, Pages 243252 (2018).
2017
W.J. Sun, S. Jiang, and K. Xu, "A Multidimensional Unified Gaskinetic Scheme for
Radiative Transfer Equations on Unstructured Mesh",
Journal of Computational Physics 351 (2017), pp. 455472.
Y.J. Zhu, Chongwen Zhong, and K. Xu,"Unified Gaskinetic 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 gaskinetic scheme for diatomic molecular
flow with translational, rotational, and vibrational modes",
Journal of Computational Physics 350 (2017), pp. 237259.
C. Liu and K. Xu,"A Unified Gas Kinetic Scheme for Continuum
and Rarefied Flows V: Multiscale and Multicomponent Plasma Transport",
Commun. Comput. Phys., Vol. 22, No. 5, pp. 11751223, November 2017 (doi: 10.4208/cicp.OA20170102).
Xiaodong Ren, Kun Xu, and Wei Shyy,
"A gaskinetic theory based multidimensional highorder method for the compressible
NavierStokes solutions", Acta Mech. Sin. (2017) 33(4): 733741.
Wei Xu, Liang Pan, Bo Gao, Yi Chiu, Kun Xu and YiKuen 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, XiaoJun 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. 398417.
W.J. Sun, S. Jiang, and K. Xu, "An Implicit Unified Gas Kinetic Scheme for Radiative Transfer
with Equilibrium and NonEquilibrium Diffusive Limits", Commun. Comput. Phys., Vol. 22 (2017), No. 4, pp. 889912,
October.
L. Pan, J.Q. Li, and K. Xu,"A Few Benchmark Test Cases for Higherorder Euler Solvers",
Numer. Math. Theor. Meth. Appl., Vol. 10, No. 4, pp. 711736, November (2017).
Liang Pan, Junxia Cheng, Shuanghu Wang, Kun Xu,
"A twostage fourthorder gaskinetic scheme for compressible multicomponent flows",
Commun. Comput. Phys., Vol. 22 (2017), No. 4, pp. 11231149, October.
Guangzhao Zhou, Kun Xu, Feng Liu,
"Simplification of the flux function for a highorder gaskinetic evolution model",
Journal of Computational Physics 339 (2017), pp. 146162.
K.Xu and C. Liu,"A Paradigm for Modeling and Computation of Gas Dynamics", Physics of Fluids 29, 026101 (2017).
K.Xu,"To overcome memory barrier of kinetic solvers for nonequilibrium flow study",
Science Bulletin 62 (2017) 99101.
T.B. Xiao, Q.D. Cai, and K.Xu,"A wellbalanced unified gaskinetic scheme for multiscale flow
transport under gravitational field", Journal of Computational Physics,
Volume 332, 1 March 2017, Pages 475491.
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), 862877.
L. Pan, K. Xu, Q.B. Li, and J.Q. Li,"An efficient and accurate twostage fourthorder
gaskinetic scheme for the Euler and NavierStokes equations",
Journal of Computational Physics 326 (2016) 197221.
R.J. Wang, X.P. Xu, K. Xu, and T.Z. Qian, "Onsager's Cross Coupling Effects in Gas Flows Confined to Microchannels", 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), 944958.
L. Pan and K. Xu,"A Thirdorder Compact Gaskinetic Scheme on Unstructured Meshes for Compressible NavierStokes Solutions", J. Comput. Phys. 318 (2016), 327348.
Xiaodong Ren, Kun Xu, and Wei Shyy, "A multidimensional highorder DGALE method based on gaskinetic theory with application to oscillating airfoils", J. Comput. Phys. 316 (2016), 700720.
Yajun Zhu, Chengwen Zhong, and Kun Xu, "Implicit unified gaskinetic scheme for steady state solution in all flow regimes", J. Comput. Phys. 315 (2016), pp. 1638.
Chang Liu, Kun Xu, Quanhua Sun, and Qingdong Cai "A unified gaskinetic scheme for continuum and rarefied flow IV: full Boltzmann and model equations", J. Comput. Phys. 314 (2016), 305340.
Lianhua Zhu, Zhaoli Guo, and Kun Xu,"Discrete unified gas kinetic scheme on unstructured meshes", Computers and Fluids 127 (2016) 211225 .
2015
L. Pan and K. Xu,"A Compact Thirdorder Gaskinetic Scheme for Compressible Euler and NavierStokes Equations", Commun. Comput. Phys., Vol. 18 (2015), No. 4, pp. 9851011.
Wenjun Sun, Song Jiang, Kun Xu, and Shu Li, "An asymptotic preserving unified gas kinetic scheme for frequencydependent radiative transfer system", J. Comput. Phys. Vol. 302 (2015), pp. 222238.
L. Pan and K. Xu,"A thirdorder gaskinetic scheme for threedimensional inviscid and viscous flow computations", Computers & Fluids 119 (2015)
250260.
Kun Xu,"Direct modeling for computational fluid dynamics", Acta Mech Sin (2015), 31(3), pp. 303318.
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 Multidimensional Highorder Discontinuous Galerkin Method Based on Gas Kinetic Theory for Viscous Flow Computations", J. Comput. Phys. Vol. 292 (2015), pp. 176193.
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. 657681.
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. 245266.
Songze Chen and Kun Xu, "A Comparative Study of an Asymptotic Preserving Scheme and Unified Gaskinetic Scheme in Continuum Flow Limit", J. Comput. Phys. Vol. 288 (2015), pp. 5265.
L. Pan, K. Xu, Generalized Coordinate Transformation and Gaskinetic Scheme, J. Comput. Phys. Vol. 287 (2015), pp. 207225.
Kun Xu and Songze Chen, Gaskinetic scheme in hypersonic flow simulation (in CHINESE), Acta Aeronautica et Astronautica Sinica, Vol. 36 (2015), pp. 135146. 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. 265279.
2014
Xu K, Li Q B, Li Z W. Direct modelingbased computational fluid dynamics (in Chinese). Sci SinPhys Mech Astron, 2014, 44: 519530, doi:
10.1360/SSPMA201300054
Ruijie Wang, Kun Xu, "Unified gaskinetic 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. 96113.
2013
Zhaoli Guo, Kun Xu, Ruijie Wang, "Discrete unified gas kinetic scheme for all Knudsen number flows: Lowspeed isothermal case", Physical Review E 88, 033305 (2013).
J. Luo and K. Xu, "A highorder multidimensional gaskinetic scheme for hydrodynamic equations", Science China, Technological Sciences, Vol. 56, No. 10, pp. 23702384, October 2013.
T. Ohwada, R. Adachi, K. Xu, J. Luo,"On the remedy against shock anomalies in kinetic schemes", J. Comput. Phys. 255 (2013), 106129.
M. Fossati, A. Guardone, L. Vigevano, and K. Xu, "Kinetic nodepair formulation for
twodimensional flows from continuum to transition regime", AIAA Journal, Vol. 51, No. 4, pp. 784796, April 2013.
J.C. Huang, K. Xu, and P.B. Yu, "A Unified Gaskinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations", Commun. Comput. Phys., vol. 14, No. 5, pp. 11471173, November, 2013.
J. Luo, L.J. Xuan, and K. Xu, "Comparison of fifthorder WENO scheme and WENOgaskinetic scheme
for inviscid and viscous flow simulation", Commun. Comput. Phys., Vol. 14, No. 3, pp. 599620, September, 2013.
L.J. Xuan and K. Xu, "A new gaskinetic scheme based on analytical solutions of the BGK equation" Journal of Computational Physics, vol. 234 (2013), 524539.
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. 66436664, August (2012).
H.W. Liu, K. Xu, T.S. Zhu, W.J. Ye, "Multiple temperature kinetic model and its applications to microscale gas flows", Computers and Fluids, vol. 67, pp. 115122, July (2012).
Q.B. Li and K. Xu, "Progress in Gaskinetic Scheme" (Review Paper in Chinese), Advances in Mechanics, vol. 42, no. 5, pp. 522537, September (2012).
R.J. Wang and K. Xu, "The study of sound wave propagation in rarefied gases using unified gaskinetic scheme",
Acta Mechanica Sinica, vol. 28(4), pp. 10221029 (2012).
J.C. Huang, K. Xu, and P.B. Yu, "A Unified Gaskinetic Scheme for Continuum and Rarefied Flows II: Multidimensional Cases", Communications in Computational Physics, vol. 12, No. 3, pp. 662690, September (2012).
2011
K. Xu and Z. Guo, "Multiple temperature gas dynamic equations for nonequilibrium flows",
J. Comput. Math, Vol. 29, No. 6, pp. 639660, 2011.
J. Luo, K. Xu, and N. Liu, "A wellbalanced symplecticitypreserving gaskinetic scheme for hydrodynamic equations under gravitational field", SIAM J. Sci. Comput. Vol. 33, No. 5, pp. 23562381, 2011.
Jiequan Li, Qibing Li, Kun Xu, "Comparison of the Generalized Riemann Solver and the GasKinetic Scheme for Inviscid Compressible Flow Simulations", Journal of Computational Physics, vol. 230 (2011), pp. 50805099.
K. Xu and J.C. Huang, "An improved unified gaskinetic scheme and the study of shock structures",
IMA J. of Applied Mathematics, vol. 76,No. 5, pp. 698711, 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. 157171, September (2011).
2010
H.W. Liu, K. Xu, T.S. Zhu, and W.J. Ye, "A multiple temperature kinetic model and its application to
microscale gas flow simulations",
conference paper for 13th Asian congress of fluid mechanics, 1721 December 2010, Dhaka, Bangladesh.
C. Jin, K. Xu, and S.Z. Chen, "A three dimensional gaskinetic scheme with moving
mesh for lowspeed viscous flow computation",
Adv. Appl. Math. Mech., vol. 2, no. 6, 746762, December, 2010.
H.Z. Tang, K. Xu, and C.P. Cai, "Gaskinetic scheme for three dimensional magnetohydrodynamics",
Numer. Math. Theor. Meth. Appl., Vol. 3, No. 4, 387404, November 2010.
K. Xu and J.C. Huang, "A unified gaskinetic scheme for continuum and rarefied flows",
J. Comput. Physics, vol. 229 (2010), pp. 77477764 (October).
Q.B. Li, K. Xu, and S. Fu, "A highorder gaskinetic NavierStokes flow solver",
J. Comput. Phys. 229 (2010), pp. 67156731 (September).
Typos in this paper
K. Xu, J. Luo, and S.Z. Chen, "A wellbalanced kinetic scheme for gas dynamic equations under gravitational field",
Advances in Applied Mathematics and Mechanics, vol. 2, no. 2, 200210, 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, 2225 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. 237240.
G. Ni, S. Jiang, and K. Xu, "Remappingfree ALEtype kinetic method for flow
computations",
J. Comput. Phys., vol. 228 (2009), pp. 31543171.
H. Luo, L. Luo, and K. Xu, "A Discontinuous Galerkin method based on
BGK scheme for the NavierStokes equations on arbitrary grids",
Advances in Applied Mathematics and Mechanics, vol. 1 (2009), pp. 301318.
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. 391401.
Z.L. Guo and K. Xu, "Generalized Gas Dynamic Equations",
47th AIAA Aerospace Sciences Meeting, AIAA 2009672 (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. 10691085.
K. Xu, X. He, C. Cai, "Multiple temperature kinetic model and gaskinetic
method for hypersonic nonequilibrium flow computations",
J. Comput. Phys., vol. 227 (2008), pp. 67796794.
K. Xu, "A generalized BhatnagarGrossKrook 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. 57995815.
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. 49554976.
C.P. Cai, D. Liu, K. Xu, "A onedimensional multipletemperature gaskinetic BGK scheme
for shock wave computation",
AIAA J.(American Institute of Aeronautics and Astronautics), vol. 46 (2008), No. 5, pp. 10541062.
Guoxi Ni, Song Jiang, K. Xu, "Efficient kinetic schemes for steady and
unsteady flow simulations on unstructured meshes", J. Comput. Phys., vol. 227, pp.30153031 (2008).
W. Liao, Y. Peng, L.S. Luo, K. Xu,
"Modified gaskinetic scheme for shock structures in argon",
Progress in Computational Fluid Dynamics, vol. 8, pp. 97108 (2008).
C.Q. Jin, K. Xu,
"Numerical study of the unsteady aerodynamics of freely falling plates",
Communications in Computational Physics, vol. 3, pp. 834851 (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. 967982, December (2007)
W. Liao, L.S. Luo, K. Xu,
"Gaskinetic scheme for continuum and nearcontinuum hypersonic flows",
J. Spacecraft and Rockets, vol. 44, No. 6, pp. 12321240, NobemberDecember (2007)
C.L. Tian, K. Xu, K.L. Chan, and L.C. Deng,
"A threedimensional multidimensional gas kinetic scheme for
the NavierStokes equations under gravitational fields",
J. Comput. Phys., vol. 226, pp. 20032027 (2007).
K. Xu and H. Liu, "Multiscale gaskinetic 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 RungeKutta Discontinuous Galerkin Method for Viscous Flow Equations",
J. Comput. Phys. 224 (2007), pp. 12231242.
Changqiu Jin and K. Xu, "A unified moving grid gaskinetic method in Eulerian
space for viscous flow computation",
J. Comput. Phys. 222 (2007), pp. 155175.
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. 858864 (2006).
K. Xu and E. Josyula,
"Continuum formulation for nonequilibrium shock structure calculation",
Communications in Computational Physics, vol. 1, No. 3, pp. 425450 (2006).
K. Xu and E. Josyula,
"Gaskinetic scheme for rarefied flow simulation",
Mathematics and Computers in Simulation 72(2006), pp.253256.
(Discrete Simulation of Fluid Dynamics in Complex Systems)
M. Torrilhon and K. Xu,
"Stability and consistency of kinetic upwinding for advectiondiffusion
equations", IMA Journal of Numerical Analysis, vol. 26, pp.686722 (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. 309340.
Changqiu Jin and K. Xu, "An adaptive grid method for two dimensional
viscous flows",
J. Comput. Phys. vol. 218, pp.6881 (2006).
Y.T. Que and K. Xu, "The study of rollwaves in inclined open channels
and solitary wave runup",
Int. J. Numer. Methods in Fluids, vol. 50, pp. 10031027 (2006).
2005
M.L. Mao, K. Xu, and X.G. Deng, "The application of gaskinetic BGK scheme in
near continuum flow regime",
Acta Aerodynamica Sinica (CHINESE), Vol. 23, No. 3, 317321 (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 NavierStokes flow solver with
scalar transport",
J. Comput. Phys., vol. 204 (2005), pp. 692714.
K. Xu, M.L. Mao, and L. Tang, "A multidimensional gaskinetic BGK scheme for hypersonic
viscous flow",
J. Comput. Phys., vol. 203 (2005), pp. 405421.
2004
T. Ohwada and K. Xu, "The kinetic scheme for full Burnett equations",
J. Comput. Phys., vol. 201 (2004), pp.315332.
K. Xu, "Discontinuous Galerkin BGK method for viscous
flow equations: onedimensional systems", SIAM
J. on Scientific Computing, Vol. 23, No. 6, pp. 19411963 (2004).
K. Xu and Z.H. Li, "Microchannel flows in slip flow regime: BGKBurnett
solutions", J. Fluid Mechanics (2004), vol. 513, pp. 87110
K. Xu and L. Tang, "Nonequilibrium BGK model for nitrogen shock structure",
Phys. of Fluids 16 (2004), pp. 3824.
2003
K. Xu and X.Y. He, "Lattice Boltzmann method and Gaskinetic BGK scheme in the low
Mach number viscous flow simulations",
J. Comput. Phys., Vol. 190, pp. 100117 (2003).
K. Xu, "SuperBurnett solutions for Poiseuille flow", Physics of
Fluids, Vol. 15, No. 7, pp. 20772080 (2003).
2002
K. Xu, "A wellbalanced gaskinteic scheme for the shallow
water equations with source terms",
J. Comput. Phys. Vol. 178 (2002), pp. 533562.
K. Xu, "Regularization of the ChapmanEnskog expansion and its
description of shock structure",
Physics of Fluids, Vol.14, No.4, pp. L17L20 (2002).
K. Xu, "A Slopeupdate Scheme for Compressible Flow Simulation",
J. Comput. Phys. Vol. 178 (2002), pp. 252259.
(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, 40:3754 (2001).
S. Lui and K. Xu, "Entropy Analysis of KFVS Schemes for the compressible Euler Equations",
Z. angew. Math. Phys., Vol. 52 (2001), pp. 6278.
(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 Godunovtype Schemes",
Int. J. Numer. Methods in Fluids, Vol. 37, pp. 122 (2001).
K. Xu, "A Gaskinetic BGK Scheme for the NavierStokes Equations, and Its Connection
with Artificial Dissipation and Godunov Method",
J. Comput. Phys., Vol. 171 (2001), pp. 289335.
Typos in the paper
Comment on "Development of an Improved Gaskinetic BGK Scheme
for Inviscid and Viscous Flows" [J. Comput. Phys., 158, 127 (2000)]
(JCP Vol. 171, pp. 843847 (2001) )
H.Z.. Tang and K.Xu, "Pseudoparticle Representation and Positivity Analysis
of Explicit and Implicit StegerWarming FVS Schemes",
Z. angew. Math. Phys. 52 (2001) 847858.
K.Xu, "A GasKinetic Method for HyperbolicElliptic Equations and Its Application in TwoPhase Flow",J. of Comput. Physics 166 (2001), No. 2, pp. 383399.
J.Q. Deng, M.S. Ghidaoui, W.G. Gray, and K. Xu,
"A Boltzmannbased Mesoscopic Model for Contaminant Transport in Flow System", Advances in Water Resources 24 (2001), pp. 531550.
Selected Publications before 2001
K. Xu, "GasKinetic Schemes for Unsteady Compressible Flow Simulations" (VKI report 199803 (1998))
H.Z. Tang and K. Xu, "A Highorder Gaskinetic Method for Multidimensional Ideal Magnetohydrodynamics",
J. Comput. Phys. 165 (2000), pp. 6988.
K. Xu, "Gaskinetic Theory based Flux Splitting Method for Ideal MHD Equations",
J. Comput. Phys. 153 (1999), pp. 334352.
K. Xu, "Gaskinetic 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 Gaskinetic Schemes for Multimaterial Flows and Its Application
in Chemical Reactions", J. Comput. Phys., Vol. 163, pp. 349375 (2000).
Y.S. Lian and K. Xu, "A Gaskinetic Scheme for Reactive Flows", Computers and Fluids, Vol. 29 (2000), pp. 725748.
K. Xu and S.H. Lui, "RayleighBernard simulation using the gaskinetic BhatnagarGrossKrook scheme
in the incompressible limit", Phy. Rev. E Vol. 60 (1999), pp. 464470.
T. Tang and K. Xu, "Gaskinetic schemes for the compressible Euler equations: positivitypreserving analysis", Z. angew. Math. Phys. Vol. 50 (1999), pp. 258281.
M. Su, K. Xu, and M.S. Ghidaoui, "Lowspeed flow simulation by gaskinetic scheme",
J. Comput. Phys., Vol. 150, pp. 1739 (1999).
K. Xu and J. Hu, "Projection dynamics in Godunovtype schemes",
J. Comput. Phys., Vol. 142, pp. 412427 (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. 11771188 (1998).
K. Xu, "BGKbased scheme for multicomponent flow calculations",
J. Comput. Phys., Vol. 134, pp. 122133 (1997).
K. Xu, C. Kim, L. Martinelli, and A. Jameson, "BGKbased 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 GasKinetic Relaxation Schemes for the Compressible Euler Equations", J. of Stat. Phys. 81, pp. 147164 (1995).
K. Xu, L. Martinelli, and A. Jameson, "Gaskinetic finite volume methods, fluxvector splitting, and artificial diffusion",
J. Comput. Phys., Vol. 120, pp. 4865 (1995).
K. Xu and K. Prendergast, "Numerical NavierStokes solutions from gaskinetic theory",
J. Comput. Phys., Vol. 114, pp. 917 (1994).
K.Prendergast and K. Xu,"Numerical hydrodynamics from gaskinetic theory",
J. Comput. Phys., Vol. 109, pp. 5366 (1993).
PhD Thesis (1993)
part 1
part 2
part 3
part 4
