研究方向：偏微分方程数值解

主要研究兴趣：计算流体力学和动理学方程的高精度数值模拟，以及传统数值算法和机器学习融合的新型算法。

近期主要研究问题：

（1）跨流域流体力学方程组的一致稳定高精度渐近保持算法

（2）多尺度动理学方程的一致稳定渐近保持间断Galerkin有限元方法

近期成果：

[1]. S. Zheng, M. Tang, Q. Zhang, and T. Xiong, High order conservative LDG-IMEX methods for the degenerate 

      nonlinear non-equilibrium radiation diffusion problems, Journal of Computational Physics,  503 (2024), 112838

[2]. W. Chen, K. Wu, and T. Xiong, High Order Structure-Preserving Finite Difference WENO Schemes for MHD 

      Equations with Gravitation in all Sonic Mach Numbers, Journal on Scientific Computing, 99 (2024), 

       https://doi.org/10.1007/s10915-024-02492-7 

[3]. Y. Shi, P. Song, and T. Xiong, An efficient asymptotic preserving Monte Carlo method for radiative transfer

      equations, Journal of Computational Physics,  493 (2023), 112483

[4]. G. Zhang, H. Zhu, and T. Xiong, Asymptotic Preserving and Uniformly Unconditionally Stable Finite 

      Difference Schemes for Kinetic TransportEquations, SIAM Journal on Scientific Computing, 

      45 (2023), B697-B730 

[5]. W. Chen, K. Wu, and T. Xiong, High order asymptotic preserving finite difference WENO schemes with 

      constrained transport for MHD equations in all sonic Mach numbers, Journal of Computational Physics,  

      488 (2023), 112240

[6]. P. Zhang and T. Xiong, High order implicit finite difference schemes with a semi-implicit WENO reconstruction 

      for nonlinear degenerate parabolic equations, Journal of Computational Physics, 467 (2022), 111442 

[7]. G. Huang, Y. Xing, and T. Xiong, High order well-balanced asymptotic preserving finite difference WENO schemes

      for the shallow water equations in all Froude numbers, Journal of Computational Physics, 463 (2022), 111255 

[8]. T. Xiong, W. Sun, Y. Shi, and P. Song, High order asymptotic preserving discontinuous Galerkin methods for 

      gray radiative transfer equations, Journal of Computational Physics, 463 (2022), 111308 

[9]. S. Boscarino, J. Qiu, G. Russo and T. Xiong, High Order Semi-implicit WENO Schemes for All-Mach Full Euler 

      System of Gas Dynamics, SIAM Journal on Scientific Computing, 44 (2022), B368-B394 

[10]. S. Boscarino, J. Qiu, G. Russo and T. Xiong, A high order semi-implicit IMEX WENO scheme for the all-Mach 

        isentropic Euler system, Journal of Computational Physics, 392 (2019), 594-618