Research

Submitted Preprints
Publications

Most up-to-date information can be found at Google Scholar.

  • J. Huang, L. Liu, K. Qi, and J. Wan. Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties, accepted by Computer Methods in Applied Mechanics and Engineering, 2025.

  • Z. Ma and J. Huang. Uniform accuracy of implicit-explicit Runge-Kutta methods for linear hyperbolic relaxation systems, Journal of Scientific Computing, 104(2), 60, 2025.

  • A. J. Christlieb, M. Ding, J. Huang, and N. A. Krupansky. Hyperbolic Machine Learning Moment Closures for the BGK Equations, SIAM Multiscale Modeling and Simulation, 23(1), 187–217, 2025.

  • M. Bauerle, A. J. Christlieb, M. Ding, and J. Huang. On the rotational invariance and hyperbolicity of shallow water moment equations in two dimensions, SIAM Journal on Mathematical Analysis, 57(1), 1039–1085, 2025.

  • Z. Ma, J. Huang, and W.-A. Yong. Uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for linear hyperbolic relaxation systems, Mathematics of Computation, 2025.

  • J. Huang, W. Guo, and Y. Cheng. Adaptive sparse grid discontinuous Galerkin method: review and software implementation, Communications on Applied Mathematics and Computation, 6(1), 501-532, 2024.

  • A. Galindo-Olarte, J. Huang, J. Ryan, and Y. Cheng. Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations, BIT Numerical Mathematics, 63(4), 52, 2023.

  • J. Huang, R. Li, and Y. Zhou. Coupling conditions for linear hyperbolic relaxation systems in two-scales problems, Mathematics of Computation, 92, 2133–2165, 2023.

  • J. Huang, T. Izgin, S. Kopecz, A. Meister, and C.-W. Shu. On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 57(2), 1063–1086, 2023.

  • F. Zhu, J. Huang, and Y. Yang. Bound-preserving discontinuous Galerkin methods with modified Patankar time integrations for chemical reacting flows, Communications on Applied Mathematics and Computation, 1–28, 2023.

  • J. Huang, Y. Cheng, A. J. Christlieb, and L. F. Roberts. Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds, Journal of Scientific Computing, 94(1), 1–27, 2023.

  • J. Huang, Y. Cheng, A. J. Christlieb, L. F. Roberts, and W.-A. Yong. Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, SIAM Multiscale Modeling and Simulation, 21(2), 489–512, 2023.

  • J. Huang, Y. Cheng, A. Christlieb, and L. Roberts. Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure, Journal of Computational Physics, 453, 110941, 2022.

  • J. Huang, Y. Liu, Y. Liu, Z. Tao, and Y. Cheng. A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations, SIAM Journal on Scientific Computing, 44(2), A745–A769, 2022.

  • J. Huang, Y. Zhou, and W.-A. Yong. Data-driven discovery of multiscale chemical reactions governed by the law of mass action, Journal of Computational Physics, 448, 110743, 2022.

  • J. Huang, Z. Ma, Y. Zhou, and W.-A. Yong. Learning thermodynamically stable and Galilean invariant partial differential equations, Journal of Non-Equilibrium Thermodynamics, 2021.

  • W. Guo, J. Huang, Z. Tao, and Y. Cheng. An adaptive sparse grid local discontinuous Galerkin method for Hamilton–Jacobi equations in high dimensions, Journal of Computational Physics, 436, 110294, 2021.

  • W. Zhao, J. Huang, and W.-A. Yong. Lattice Boltzmann method for stochastic convection diffusion equations, SIAM/ASA Journal on Uncertainty Quantification, 9(2), 536–563, 2021.

  • Z. Tao, J. Huang, Y. Liu, W. Guo, and Y. Cheng. An adaptive multiresolution ultra-weak discontinuous Galerkin method for Schrödinger equations, Communications on Applied Mathematics and Computation, 1–24, 2020.

  • J. Huang, Y. Liu, W. Guo, Z. Tao, and Y. Cheng. An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form, Journal of Scientific Computing, 85, 2020.

  • W. Zhao and J. Huang. Boundary treatment of implicit-explicit Runge-Kutta method for hyperbolic systems with source terms, Journal of Computational Physics, 423, 109828, 2020.

  • W. Zhao, J. Huang, and S. J. Ruuth. Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws, Journal of Computational Physics, 421, 109697, 2020.

  • J. Huang and Y. Cheng. An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensions, SIAM Journal on Scientific Computing, 42(5), A2943–A2973, 2020.

  • W. Zhao, J. Huang, and W.-A. Yong. Boundary conditions for kinetic theory based models I: lattice Boltzmann models, SIAM Multiscale Modeling and Simulation, 17(2), 854–872, 2019.

  • J. Huang, W. Zhao, and C.-W. Shu. A third-order unconditionally positivity-preserving scheme for production–destruction equations with applications to non-equilibrium flows, Journal of Scientific Computing, 79, 1015–1056, 2019.

  • J. Huang and C.-W. Shu. Positivity-preserving time discretizations for production–destruction equations with applications to non-equilibrium flows, Journal of Scientific Computing, 78, 1811–1839, 2019.

  • J. Huang and C.-W. Shu. Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms, Journal of Computational Physics, 361, 111–135, 2018.

  • J. Huang and C.-W. Shu. A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model, Mathematical Models and Methods in Applied Sciences, 27(3), 549–579, 2017.

  • J. Huang and C.-W. Shu. Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, Numerical Methods for Partial Differential Equations, 33(2), 467–488, 2017.

  • Z.-X. Hu, J. Huang, W.-X. Huang, and G.-X. Cui. Second-order curved interface treatments of the lattice Boltzmann method for convection-diffusion equations with conjugate interfacial conditions, Computers & Fluids, 144, 60–73, 2017.

  • Z. Hu, J. Huang, and W.-A. Yong. Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, Physical Review E, 93(4), 043320, 2016.

  • J. Huang, Z. Hu, and W.-A. Yong. Second-order curved boundary treatments of the lattice Boltzmann method for convection-diffusion equations, Journal of Computational Physics, 310, 26–44, 2016.

  • J. Huang, L. Hong, and W.-A. Yong. Generalization of the Kullback–Leibler divergence in the Tsallis statistics, Journal of Mathematical Analysis and Applications, 436(1), 501–512, 2016.

  • J. Huang and W.-A. Yong. Boundary conditions of the lattice Boltzmann method for convection-diffusion equations, Journal of Computational Physics, 300, 70–91, 2015.

  • J. Huang, H. Wu, and W.-A. Yong. On initial conditions for the lattice Boltzmann method, Communications in Computational Physics, 18(2), 450–468, 2015.

  • J. Huang, L. Zhang, W.-A. Yong, and M. Wang. On complex boundary conditions of the lattice Boltzmann method for the diffusion equations, Applied Mathematics and Mechanics (Chinese Edition), 35(3), 305–312, 2014.