Nonlinear Stability and Structure Preservation | Kailiang Wu

On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws

@article{pub2023geometricquasilinearizationframeworkforanalysisanddesignofbound,
  author = {Kailiang Wu and Chi-Wang Shu},
  title = {{Geometric quasilinearization framework for analysis and design of bound-preserving schemes}},
  journal = {SIAM Review},
  year = {2023},
  volume = {65},
  number = {4},
  pages = {1031--1073},
  doi = {10.1137/21M1458247},
  eprint = {2111.04722},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1137/21M1458247}
}

S. Cui, S. Ding, and K. Wu*

SIAM Journal on Numerical Analysis, 2024.

BibTeX

Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics

@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}
}

K. Wu

SIAM Journal on Numerical Analysis, 2018.

Paper PDF arXiv

BibTeX

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

@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}
}

K. Wu and H. Tang

Math. Models Methods Appl. Sci. (M3AS), 2017.

BibTeX

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

@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}
}

K. Wu* and C.-W. Shu

Numerische Mathematik, 2019.

BibTeX

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

@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}
}

K. Wu

SIAM Journal on Scientific Computing, 2021.

BibTeX

OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws

@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}
}

M. Peng, Z. Sun, and K. Wu*

Mathematics of Computation, 2025.

Paper PDF (arXiv version) arXiv

BibTeX

EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression

@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}
}

K. Wu

arXiv, 2026. Preprint

BibTeX

Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework

@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}
}

H. Cao, K. Wu*, and C. Yuan

arXiv, 2026. Preprint

BibTeX

Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO–TV Conjecture and Shift Cohomology

@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}
}

Z. Li and K. Wu*

arXiv, 2026. Preprint

BibTeX

High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations

@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}
}

L. Xu and K. Wu*

arXiv, 2026. Preprint

BibTeX

On local minimum entropy principle of high-order schemes for relativistic Euler equations

@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}
}

S. Cui, K. Wu*, and L. Xu

Mathematics of Computation, 2026.

BibTeX

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

@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}
}

K. Wu and C.-W. Shu

SIAM Journal on Scientific Computing, 2020.

BibTeX

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

@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}
}

Z. Sun, Y. Wei, and K. Wu*

SIAM Journal on Numerical Analysis, 2022.

BibTeX

On energy laws and stability of first-subdiagonal Padé approximants for linear seminegative problems

@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}
}

M. Jiao, Z. Sun, and K. Wu*

Journal of Information and Computing Science, 2026. Accepted

BibTeX

Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?

@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}
}

S. Cui, S. Ding, and K. Wu*

Journal of Computational Physics, 2023.

BibTeX

Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes

@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}
}

S. Ding, S. Cui, R. Abgrall, and K. Wu*

arXiv, 2026. Preprint

BibTeX

A novel and simple invariant-domain-preserving framework for PAMPA scheme: 1D case

@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}
}

R. Abgrall, M. Jiao, Y. Liu, and K. Wu*

SIAM Journal on Scientific Computing, 2025.

BibTeX

Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case

@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}
}

R. Abgrall, M. Jiao, Y. Liu*, and K. Wu

Communications in Computational Physics, 2026.

BibTeX

Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws

@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}
}

S. Cui, A. Kurganov, and K. Wu*

SIAM Journal on Scientific Computing, 2024.

BibTeX

Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations

@article{pub2024boundpreservingframeworkforcentralupwindschemesforgeneral,
  author = {Shumo Cui and Alexander Kurganov and Kailiang Wu},
  title = {{Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws}},
  journal = {SIAM Journal on Scientific Computing},
  year = {2024},
  volume = {46},
  number = {5},
  pages = {A2899--A2924},
  doi = {10.1137/23M1628024},
  eprint = {2403.13420},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1137/23M1628024}
}

S. Cui, Y. Gu, A. Kurganov*, K. Wu, and R. Xin

Journal of Computational Physics, 2025.

BibTeX

Bound-preserving OEDG schemes for Aw–Rascle–Zhang traffic models on networks

@article{pub2025positivitypreservingnewlowdssipationcentralupwindschemesfor,
  author = {S. Cui and Y. Gu and A. Kurganov and K. Wu and R. Xin},
  title = {{Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations}},
  journal = {Journal of Computational Physics},
  year = {2025},
  doi = {10.1016/j.jcp.2025.114189},
  url = {https://doi.org/10.1016/j.jcp.2025.114189}
}

W. Chen, S. Cui*, K. Wu, and T. Xiong

Journal of Computational Physics, 2025.

BibTeX

COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods

@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}
}

H. Cao, Y. Huang, Z. Li, and K. Wu*

Journal of Computational Physics, 2026.

BibTeX

COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws

@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}
}

R. Yan, H. Cao, N. Liu*, and K. Wu

Journal of Computational Physics, 2027.

BibTeX

Runge–Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes

@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}
}

M. Peng, Z. Li, and K. Wu*

arXiv, 2026. Preprint

BibTeX

Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws

@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}
}

M. Peng, K. Wu*, and C. Yuan

SIAM Journal on Scientific Computing, 2026.

BibTeX

Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates

@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}
}

Z. Li and K. Wu*

SIAM Journal on Scientific Computing, 2025.

BibTeX

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

@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}
}

C. Fan and K. Wu*

Journal of Computational Physics, 2024.

BibTeX

Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition

@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}
}

S. Ding, S. Cui, and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws

@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}
}

C. Fan and K. Wu*

arXiv, 2026. Preprint

BibTeX

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

@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}
}

K. Wu* and C.-W. Shu

Numerische Mathematik, 2021.

BibTeX

Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations

@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}
}

K. Wu*, H. Jiang, and C.-W. Shu

SIAM Journal on Numerical Analysis, 2023.

BibTeX

A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations

@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}
}

S. Ding and K. Wu*

SIAM Journal on Scientific Computing, 2024.

BibTeX

A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics

@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}
}

A. Chertock, A. Kurganov*, M. Redle, and K. Wu

SIAM Journal on Scientific Computing, 2024.

BibTeX

GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics

@article{pub2024anewlocallydivergencefreepathconservativecentralupwind,
  author = {Alina Chertock and Alexander Kurganov and Michael Redle and Kailiang Wu},
  title = {{A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics}},
  journal = {SIAM Journal on Scientific Computing},
  year = {2024},
  volume = {46},
  number = {3},
  pages = {A1998--A2024},
  doi = {10.1137/22M1539009},
  eprint = {2212.02682},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1137/22M1539009}
}

S. Ding and K. Wu*

Journal of Computational Physics, 2024.

BibTeX

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving

@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}
}

M. Liu and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation

@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}
}

M. Liu, K. Wu, and C. Yuan*

Journal of Computational Physics, 2026.

BibTeX

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system

@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}
}

R. Yan, H. Cao, and K. Wu*

Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted

BibTeX

An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint

@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}
}

M. Liu, D. Pang, R. Abgrall, and K. Wu*

Journal of Computational Physics, 2026. In press

BibTeX

Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics

@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}
}

D. Pang and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

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

@article{pub2025provablypositivitypreservingconstrainedtransportschemefor2dand3didealmagnetohydrodynamics,
  author = {Dongwen Pang and Kailiang Wu},
  title = {{Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics}},
  journal = {Journal of Computational Physics},
  year = {2025},
  volume = {541},
  pages = {114312},
  eprint = {2410.05173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2410.05173}
}

K. Wu and H. Tang

Z. Angew. Math. Phys., 2018.

BibTeX

A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics

@article{pub2018onphysicalconstraintspreservingschemesforspecialrelativisticmagnetohydrodynamicswithageneral,
  author = {Kailiang Wu and Huazhong Tang},
  title = {{On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state}},
  journal = {Z. Angew. Math. Phys.},
  year = {2018},
  volume = {69},
  pages = {84},
  eprint = {1709.05838},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1709.05838}
}

K. Wu and C.-W. Shu

SIAM Journal on Scientific Computing, 2018.

BibTeX

High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers

@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}
}

W. Chen, K. Wu, and T. Xiong

Journal of Scientific Computing, 2024.

BibTeX

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

@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}
}

W. Chen, K. Wu, and T. Xiong

Journal of Computational Physics, 2023.

BibTeX

Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity

@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}
}

S. Ding, K. Wu*, and C. Yuan

Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.

BibTeX

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

@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}
}

K. Wu

Physical Review D, 2017.

BibTeX

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

@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}
}

K. Wu and H. Tang

Astrophys. J. Suppl. Ser. (ApJS), 2017.

BibTeX

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

@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}
}

K. Wu and H. Tang

Journal of Computational Physics, 2015.

BibTeX

Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics

@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}
}

H. Cao, M. Peng, and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions

@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}
}

L. Xu, S. Ding, and K. Wu*

Journal of Computational Physics, 2026. Accepted

BibTeX

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

@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}
}

Y. Chen and K. Wu*

Journal of Computational Physics, 2022.

BibTeX

High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics

@article{pub2022aphysicalconstraintpreservingfinitevolumemethodforspecial,
  author = {Yaping Chen and Kailiang Wu},
  title = {{A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes}},
  journal = {Journal of Computational Physics},
  year = {2022},
  volume = {466},
  pages = {111398},
  eprint = {2207.09385},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2207.09385}
}

C. Yuan, Z. Zhang, H. Tang, and K. Wu*

Journal of Computational Physics, 2026.

BibTeX

High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state

@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}
}

L. Xu, S. Ding, and K. Wu*

Journal of Scientific Computing, 2024.

BibTeX

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

@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}
}

C. Cai, J. Qiu, and K. Wu*

Journal of Computational Physics, 2024.

BibTeX

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

@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}
}

K. Wu and Y. Xing

SIAM Journal on Scientific Computing, 2021.

BibTeX

On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation

@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}
}

Y. Ren, K. Wu, J. Qiu, and Y. Xing

Journal of Computational Physics, 2023.

BibTeX

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

@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}
}

H. Jiang, H. Tang, and K. Wu*

Journal of Computational Physics, 2022.

BibTeX

High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity

@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}
}

Z. Zhang, H. Tang, and K. Wu*

Journal of Computational Physics, 2025.

BibTeX

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms

@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}
}

J. Wang, H. Tang, and K. Wu*

Journal of Computational Physics, 2024.

BibTeX

Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics

@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}
}

L. Y. Win, Y. Chen*, Y. Nie, L. Cai, and K. Wu

Journal of Scientific Computing, 2025.

BibTeX

Uniformly high-order bound-preserving OEDG schemes for two-phase flows

@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}
}

R. Yan, R. Abgrall, and K. Wu*

Math. Models Methods Appl. Sci. (M3AS), 2024.

BibTeX

Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows

@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}
}

J. Du, C. Fan, and K. Wu

Annals of Applied Mathematics, 2024.

BibTeX

Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System

@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}
}

Y. Huang, M. Peng, and K. Wu*

Communications in Mathematical Research, 2025.

BibTeX

Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations

@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}
}

C. Fan, Q. Huang, and K. Wu*

arXiv, 2025. Preprint

BibTeX

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

@misc{pubarxiv251018380,
  author = {Chuan Fan and Qian Huang and Kailiang Wu},
  title = {{Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations}},
  year = {2025},
  eprint = {2510.18380},
  archivePrefix = {arXiv},
  note = {Preprint},
  url = {https://arxiv.org/abs/2510.18380}
}

K. Wu, T. Qin, and D. Xiu

SIAM Journal on Scientific Computing, 2020.

BibTeX

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

@article{pub2020structurepreservingmethodforreconstructingunknownhamiltoniansystemsfrom,
  author = {Kailiang Wu and Tong Qin and Dongbin Xiu},
  title = {{Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data}},
  journal = {SIAM Journal on Scientific Computing},
  year = {2020},
  volume = {42},
  number = {6},
  pages = {A3704--A3729},
  eprint = {1905.10396},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.10396}
}

K. Wu, H. Tang, and D. Xiu

Journal of Computational Physics, 2017.

BibTeX