High-Order Accurate Numerical Methods | Kailiang Wu
Kailiang Wu
Professor of Mathematics
Southern University of Science and Technology (SUSTech)
Email: wukl@sustech.edu.cn
Mailing address
Department of Mathematics, School of Science
Southern University of Science and Technology
1088 Xueyuan Avenue, Nanshan District
Shenzhen, Guangdong 518055, China
High-Order Accurate Numerical Methods
SIAM Journal on Numerical Analysis, 2024.
arXiv
BibTeX
@article{pub2024onoptimalcellaveragedecompositionforhighorderbound,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws}},
journal = {SIAM Journal on Numerical Analysis},
year = {2024},
eprint = {2212.05045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2212.05045}
}
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
SIAM Journal on Scientific Computing, 2018.
arXiv
BibTeX
@article{pub2018aprovablypositivediscontinuousgalerkinmethodformultidimensionalideal,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2018},
volume = {40},
number = {5},
pages = {B1302--B1329},
eprint = {1807.00246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.00246}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}
SIAM Journal on Numerical Analysis, 2022.
arXiv
BibTeX
@article{pub2022onenergylawsandstabilityofrungekuttamethods,
author = {Zheng Sun and Yuanzhe Wei and Kailiang Wu},
title = {{On energy laws and stability of Runge--Kutta methods for linear seminegative problems}},
journal = {SIAM Journal on Numerical Analysis},
year = {2022},
volume = {60},
number = {5},
pages = {2448--2481},
eprint = {2201.06501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2201.06501}
}
Journal of Computational Physics, 2023.
Paper
arXiv
BibTeX
@article{pub2022istheclassicconvexdecompositionoptimalforboundpreserving,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {476},
pages = {111882},
doi = {10.1016/j.jcp.2022.111882},
eprint = {2207.08849},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2022.111882}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260631931,
author = {Manting Peng and Kailiang Wu},
title = {{Hidden Accuracy and Superconvergence Analysis of Central Discontinuous Galerkin Methods on Overlapping Meshes}},
year = {2026},
eprint = {2606.31931},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2606.31931}
}
On energy laws and stability of first-subdiagonal Padé approximants for linear seminegative problems
Journal of Information and Computing Science, 2026. Accepted
arXiv
BibTeX
@article{pub2026onenergylawsandstabilityoffirstsubdiagonalpadeapproximantsforlinear,
author = {Miaosen Jiao and Zheng Sun and Kailiang Wu},
title = {{On energy laws and stability of first-subdiagonal Pad{\'e} approximants for linear seminegative problems}},
journal = {Journal of Information and Computing Science},
year = {2026},
eprint = {2608.09239},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2608.09239}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260400301,
author = {Kailiang Wu},
title = {{EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression}},
year = {2026},
eprint = {2604.00301},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2604.00301}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026cosdgaconvexoscillationsuppressingframeworkforhighorderdiscontinuousgalerkin,
author = {Huihui Cao and Yunqing Huang and Zhuoyun Li and Kailiang Wu},
title = {{COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114755},
doi = {10.1016/j.jcp.2026.114755},
url = {https://doi.org/10.1016/j.jcp.2026.114755}
}
Journal of Computational Physics, 2027.
Paper
BibTeX
@article{pub2026cossvconvexoscillationsuppressingspectralvolumeschemeswithboundpreservationfor,
author = {Ruifang Yan and Huihui Cao and Na Liu and Kailiang Wu},
title = {{COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws}},
journal = {Journal of Computational Physics},
year = {2027},
volume = {568},
pages = {115411},
doi = {10.1016/j.jcp.2026.115411},
url = {https://doi.org/10.1016/j.jcp.2026.115411}
}
SIAM Journal on Scientific Computing, 2025.
Paper
arXiv
BibTeX
@article{pub2024spectralvolumefromadgperspectiveoscillationeliminationstability,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
volume = {47},
number = {2},
pages = {A1304-A1333},
doi = {10.1137/24m167799x},
eprint = {2409.10871},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24m167799x}
}
SIAM Journal on Scientific Computing, 2026.
Paper
arXiv
BibTeX
@article{pub2025oscillationeliminatingcentraldgschemesforhyperbolicconservationlaws,
author = {Manting Peng and Kailiang Wu and Caiyou Yuan},
title = {{Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2026},
volume = {48},
number = {2},
pages = {A695-A725},
doi = {10.1137/25m1730697},
eprint = {2503.12473},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/25m1730697}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926195,
author = {Manting Peng and Zhuoyun Li and Kailiang Wu},
title = {{Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes}},
year = {2026},
eprint = {2609.26195},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26195}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024highorderoscillationeliminatinghermitewenomethodforhyperbolic,
author = {Chuan Fan and Kailiang Wu},
title = {{High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {519},
pages = {113435},
doi = {10.1016/j.jcp.2024.113435},
eprint = {2409.09632},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113435}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926194,
author = {Chuan Fan and Kailiang Wu},
title = {{Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws}},
year = {2026},
eprint = {2609.26194},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26194}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdgschemesonunstructuredtriangularmeshesoscillationelimination,
author = {Shengrong Ding and Shumo Cui and Kailiang Wu},
title = {{Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09620}
}
Math. Models Methods Appl. Sci. (M3AS), 2024.
Paper
BibTeX
@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
author = {R. Yan and R. Abgrall and K. Wu},
title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2024},
doi = {10.1142/S0218202524500544},
url = {https://doi.org/10.1142/S0218202524500544}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Communications in Mathematical Research, 2025.
Paper
arXiv
BibTeX
@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
author = {Yuchen Huang and Manting Peng and Kailiang Wu},
title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
journal = {Communications in Mathematical Research},
year = {2025},
volume = {41},
number = {4},
pages = {370--414},
doi = {10.4208/cmr.2025-0052},
eprint = {2512.03496},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cmr.2025-0052}
}
Annals of Applied Mathematics, 2024.
Paper
BibTeX
@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
author = {J. Du and C. Fan and K. Wu},
title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
journal = {Annals of Applied Mathematics},
year = {2024},
volume = {40},
pages = {412-444},
doi = {10.4208/aam.oa-2024-0029},
url = {https://doi.org/10.4208/aam.oa-2024-0029}
}
Journal of Computational Physics, 2025.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {520},
pages = {113507},
doi = {10.1016/j.jcp.2024.113507},
eprint = {2409.16269},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113507}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260910476,
author = {Shengrong Ding and Shumo Cui and Remi Abgrall and Kailiang Wu},
title = {{Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes}},
year = {2026},
eprint = {2609.10476},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.10476}
}
SIAM Journal on Scientific Computing, 2025.
arXiv
BibTeX
@article{pub2025anovelandsimpleinvariantdomainpreservingframeworkfor,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{A novel and simple invariant-domain-preserving framework for PAMPA scheme: 1D case}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
eprint = {2412.03423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2412.03423}
}
Communications in Computational Physics, 2026.
Paper
arXiv
BibTeX
@article{pub2025boundpreservingpointaveragemomentpolynomialinterpretedpampaschemeonedimensionalcase,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case}},
journal = {Communications in Computational Physics},
year = {2026},
volume = {39},
number = {1},
pages = {29-58},
doi = {10.4208/cicp.oa-2024-0266},
eprint = {2410.14292},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cicp.oa-2024-0266}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260719283,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO--TV Conjecture and Shift Cohomology}},
year = {2026},
eprint = {2607.19283},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2607.19283}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926791,
author = {Huihui Cao and Kailiang Wu and Caiyou Yuan},
title = {{Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework}},
year = {2026},
eprint = {2609.26791},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26791}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260809327,
author = {Linfeng Xu and Kailiang Wu},
title = {{High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations}},
year = {2026},
eprint = {2608.09327},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2608.09327}
}
Mathematics of Computation, 2026.
Paper
arXiv
BibTeX
@article{pub2025onlocalminimumentropyprincipleofhighorderschemes,
author = {Shumo Cui and Kailiang Wu and Linfeng Xu},
title = {{On local minimum entropy principle of high-order schemes for relativistic Euler equations}},
journal = {Mathematics of Computation},
year = {2026},
volume = {95},
number = {362},
pages = {2739-2787},
doi = {10.1090/mcom/4139},
eprint = {2503.12465},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/4139}
}
Numerische Mathematik, 2021.
arXiv
BibTeX
@article{pub2021provablyphysicalconstraintpreservingdiscontinuousgalerkinmethodsformultidimensional,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations}},
journal = {Numerische Mathematik},
year = {2021},
volume = {148},
pages = {699--741},
eprint = {2002.03371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.03371}
}
SIAM Journal on Numerical Analysis, 2023.
arXiv
BibTeX
@article{pub2023provablypositivecentraldiscontinuousgalerkinschemesviageometricquasilinearization,
author = {Kailiang Wu and Haili Jiang and Chi-Wang Shu},
title = {{Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations}},
journal = {SIAM Journal on Numerical Analysis},
year = {2023},
volume = {61},
pages = {250--285},
eprint = {2203.14853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2203.14853}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewdiscretelydivergencefreepositivitypreservinghighorder,
author = {Shengrong Ding and Kailiang Wu},
title = {{A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {1},
pages = {A50--A79},
doi = {10.1137/23M1562081},
eprint = {2305.14820},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1562081}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024gqlbasedboundpreservingandlocallydivergencefreecentral,
author = {Shengrong Ding and Kailiang Wu},
title = {{GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {514},
pages = {113208},
doi = {10.1016/j.jcp.2024.113208},
eprint = {2402.15437},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113208}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}
Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.
Paper
BibTeX
@article{pub2025divergencefreefinitevolumewenoschemeforrelativisticmagnetohydrodynamics,
author = {S. Ding and K. Wu and C. Yuan},
title = {{Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity}},
journal = {Monthly Notices of the Royal Astronomical Society (MNRAS)},
year = {2025},
doi = {10.1093/mnras/staf280},
url = {https://doi.org/10.1093/mnras/staf280}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderpositivitypreservingandgloballydivergencefreediscontinuousgalerkinmethodsfor,
author = {Mengqing Liu and Kailiang Wu and Caiyou Yuan},
title = {{High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {562},
pages = {115031},
doi = {10.1016/j.jcp.2026.115031},
url = {https://doi.org/10.1016/j.jcp.2026.115031}
}
Journal of Scientific Computing, 2024.
Paper
BibTeX
@article{pub2024highorderstructurepreservingfinitedifferencewenoschemeformhdequationswith,
author = {W. Chen and K. Wu and T. Xiong},
title = {{High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {99},
pages = {36},
doi = {10.1007/s10915-024-02492-7},
url = {https://doi.org/10.1007/s10915-024-02492-7}
}
Journal of Computational Physics, 2023.
arXiv
BibTeX
@article{pub2023highorderasymptoticpreservingfinitedifferencewenoschemeswith,
author = {Wei Chen and Kailiang Wu and Tao Xiong},
title = {{High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {488},
pages = {112240},
eprint = {2211.16655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2211.16655}
}
Astrophys. J. Suppl. Ser. (ApJS), 2017.
arXiv
BibTeX
@article{pub2017physicalconstraintpreservingcentraldiscontinuousgalerkinmethodsforspecial,
author = {Kailiang Wu and Huazhong Tang},
title = {{Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state}},
journal = {Astrophys. J. Suppl. Ser. (ApJS)},
year = {2017},
volume = {228},
number = {1},
pages = {3},
eprint = {1607.08332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1607.08332}
}
Journal of Computational Physics, 2015.
arXiv
BibTeX
@article{pub2015highorderaccuratephysicalconstraintspreservingfinitedifferenceweno,
author = {Kailiang Wu and Huazhong Tang},
title = {{High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2015},
volume = {298},
pages = {539--564},
eprint = {1504.07707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1504.07707}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Journal of Computational Physics, 2026. Accepted
arXiv
BibTeX
@article{pub2026gqlbasedphysicalconstraintpreservinghighorderfinitedifferenceschemesforspecial,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions}},
journal = {Journal of Computational Physics},
year = {2026},
eprint = {2606.31992},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2606.31992}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderaccurateboundpreservingadaptivemovingmeshfinitevolumemethodsfor,
author = {C. Yuan and Z. Zhang and H. Tang and K. Wu},
title = {{High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114728},
doi = {10.1016/j.jcp.2026.114728},
url = {https://doi.org/10.1016/j.jcp.2026.114728}
}
Physical Review D, 2017.
Paper
arXiv
BibTeX
@article{pub2017designofprovablyphysicalconstraintpreservingmethodsforgeneral,
author = {Kailiang Wu},
title = {{Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics}},
journal = {Physical Review D},
year = {2017},
doi = {10.1103/PhysRevD.95.103001},
eprint = {1610.06274},
archivePrefix = {arXiv},
url = {https://doi.org/10.1103/PhysRevD.95.103001}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020entropysymmetrizationandhighorderaccurateentropystablenumerical,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {4},
pages = {A2230--A2261},
eprint = {1907.07467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1907.07467}
}
Journal of Scientific Computing, 2024.
arXiv
BibTeX
@article{pub2024highorderaccurateentropystableschemesforrelativistichydrodynamicswithageneral,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {98},
pages = {43},
eprint = {2409.10872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.10872}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024provablyconvergentnewtonraphsonmethodsforrecoveringprimitivevariables,
author = {Chaoyi Cai and Jianxian Qiu and Kailiang Wu},
title = {{Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {498},
pages = {112669},
doi = {10.1016/j.jcp.2023.112669},
eprint = {2305.14805},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112669}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021uniformlyhighorderstructurepreservingdiscontinuousgalerkinmethodsfor,
author = {Kailiang Wu and Yulong Xing},
title = {{Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {1},
pages = {A472--A510},
eprint = {2005.07166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2005.07166}
}
Journal of Computational Physics, 2023.
Paper
BibTeX
@article{pub2023onpositivitypreservingwellbalancedfinitevolumemethodsfor,
author = {Y. Ren and K. Wu and J. Qiu and Y. Xing},
title = {{On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {492},
pages = {112429},
doi = {10.1016/j.jcp.2023.112429},
url = {https://doi.org/10.1016/j.jcp.2023.112429}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022positivitypreservingwellbalancedcentraldiscontinuousgalerkinschemesfor,
author = {Haili Jiang and Huazhong Tang and Kailiang Wu},
title = {{Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {463},
pages = {111297},
eprint = {2207.09398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09398}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025highorderaccuratestructurepreservingfinitevolumeschemeson,
author = {Zhihao Zhang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09600}
}
Journal of Computational Physics, 2024.
arXiv
BibTeX
@article{pub2024highorderaccuratepositivitypreservingandwellbalanceddiscontinuous,
author = {Jiangfu Wang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms}},
journal = {Journal of Computational Physics},
year = {2024},
eprint = {2402.15446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2402.15446}
}
Journal of Scientific Computing, 2025.
Paper
BibTeX
@article{pub2025physicalconstraintpreservinghighorderfinitevolumewenomethodviageometricquasilinearization,
author = {L. Y. Win and Y. Chen and Y. Nie and L. Cai and K. Wu},
title = {{Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics}},
journal = {Journal of Scientific Computing},
year = {2025},
volume = {105},
pages = {33},
doi = {10.1007/s10915-025-03059-w},
url = {https://doi.org/10.1007/s10915-025-03059-w}
}
Numer. Math. Theor. Meth. Appl., 2017.
Paper
arXiv
BibTeX
@article{pub2017rungekuttadiscontinuouslocalevolutiongalerkinmethodsfortheshallowwaterequations,
author = {Yangyu Kuang and Kailiang Wu and Huazhong Tang},
title = {{Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid}},
journal = {Numer. Math. Theor. Meth. Appl.},
year = {2017},
volume = {10},
number = {2},
pages = {373--419},
doi = {10.4208/nmtma.2017.s09},
eprint = {1608.06700},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/nmtma.2017.s09}
}
Communications in Computational Physics, 2021.
Paper
BibTeX
@article{pub2021awenobasedstochasticgalerkinschemeforidealmhdequationswithrandom,
author = {K. Wu and D. Xiu and X. Zhong},
title = {{A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs}},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {2},
pages = {423--447},
doi = {10.4208/cicp.OA-2020-0167},
url = {https://doi.org/10.4208/cicp.OA-2020-0167}
}
Journal of Computational Physics, 2017.
Paper
arXiv
BibTeX
@article{pub2017astochasticgalerkinmethodforfirstorderquasilinearhyperbolic,
author = {Kailiang Wu and Huazhong Tang and Dongbin Xiu},
title = {{A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty}},
journal = {Journal of Computational Physics},
year = {2017},
volume = {345},
pages = {224--244},
doi = {10.1016/j.jcp.2017.05.027},
eprint = {1601.04121},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2017.05.027}
}
SIAM Journal on Scientific Computing, 2017.
Paper
BibTeX
@article{pub2017arandomizedtensorquadraturemethodforhighdimensionalpolynomial,
author = {K. Wu and Y. Shin and D. Xiu},
title = {{A randomized tensor quadrature method for high dimensional polynomial approximation}},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {5},
pages = {A1811--A1833},
doi = {10.1137/16M1081695},
url = {https://doi.org/10.1137/16M1081695}
}
Journal of Computational Physics, 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemefor,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics}},
journal = {Journal of Computational Physics},
year = {2014},
volume = {264},
pages = {177--208},
doi = {10.1016/j.jcp.2014.01.041},
url = {https://doi.org/10.1016/j.jcp.2014.01.041}
}
East Asian J. Appl. Math., 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemeforonedimensionalrelativistic,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics}},
journal = {East Asian J. Appl. Math.},
year = {2014},
volume = {4},
number = {2},
pages = {95--131},
doi = {10.4208/eajam.101013.100314a},
url = {https://doi.org/10.4208/eajam.101013.100314a}
}