个人简介
蔡晓峰博士是北京师范大学 和 北师港浸大 助理教授。研究领域是计算流体力学，主要从事针对对流占优问题的高效稳健可靠的数值方法研究。在Journal of Computational Physics(7篇)、SIAM Journal on Scientific Computing(2篇)、Mathematics of Computation、Computer Methods in Applied Mechanics and Engineering等权威期刊发表20篇学术论文。
研究领域
计算流体力学
高分辨率高精度计算方法，包括：间断有限元、加权本质无振荡格式
半拉格朗日算法
Eulerian-Lagrangian 间断Galerkin有限元方法、自适应移动网格方法、Arbitrary Lagrangian-Eulerian 方法
等离子物理模拟的高效高精度保结构数值算法
应用，包括：数值天气预报、环境流体力学等
最优控制问题
近期论文
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Eulerian-Lagrangian high order Runge-Kutta discontinuous Galerkin method
Xiaofeng Cai, Jing-Mei Qiu, Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method for transport simulations on unstructured meshes, SIAM Journal on Scientific Computing, 44(4): A2037-A2060, 2022.
Xiaofeng Cai, Jing-Mei Qiu and Yang Yang, An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics, Journal of Computational Physics, 439, 110392, 2021.
high order semi-Lagrangian discontinuous Galerkin method
Xiaofeng Cai, Wei Guo, and Jing-Mei Qiu, A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations. Journal of Scientific Computing, 2017, 73(2): 514-542.
Xiaofeng Cai, Sebastiano Boscarino and Jing-Mei Qiu, High Order Semi-Lagrangian Discontinuous Galerkin Method Coupled with Runge-Kutta Exponential Integrators for Nonlinear Vlasov Dynamics, Journal of Computational Physics, 427, 110036, 2021.
Yang Yang, Xiaofeng Cai and Jing-Mei Qiu, Optimal convergence and superconvergence of semi-Lagrangian discontinuous Galerkin methods for linear convection equations in one space dimension, Mathematics of Computation, 89(325):2113-2139, 2020.
Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting, Journal of Computational Physics, 354 (2018): 529-551.
Mingchang Ding, Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A semi-Lagrangian discontinuous Galerkin (DG) - local DG method for solving convection-diffusion equations, Journal of Computational Physics, 409 (2020): 109295.
Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, A high order semi-Lagrangian discontinuous Galerkin method for the two-dimensional incompressible Euler equations and the guiding center Vlasov model without operator splitting, Journal of Scientific Computing, 79.2 (2019): 1111-1134.
Xiaofeng Cai, Wei Guo and Jing-Mei Qiu, Comparison of semi-Lagrangian discontinuous Galerkin schemes for linear and nonlinear transport simulations, Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967-020-00088-0.
High order conservative semi-Lagrangian schemes
Hongtao Liu, Xiaofeng Cai, Yong Cao, Giovanni Lapenta, An efficient energy conserving semi-Lagrangian kinetic scheme for the Vlasov-Ampère system, Journal of Computational Physics
Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, and Jianxian Qiu, A fourth-order conservative semi-Lagrangian finite volume WENO scheme without operator splitting for kinetic and fluid simulations, Computer Methods in Applied Mechanics and Engineering Volume 395, 15 May 2022, 114973.
Hermite WENO schemes
Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, A conservative semi-Lagrangian HWENO method for the Vlasov equation, Journal of Computational Physics, 323 (2016): 95-114.
Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu and Jianxian Qiu, A conservative semi-Lagrangian hybrid Hermite WENO scheme for linear transport equations and the nonlinear Vlasov-Poisson system, SIAM Journal on Scientific Computing, to appear.
Xiaofeng Cai, Jun Zhu and Jianxian Qiu, Hermite WENO schemes with strong stability preserving multi-step temporal discretization methods for conservation laws, Journal of Computational Mathematics, 35 (2017): 19-40.
Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, Finite volume HWENO schemes for nonconvex conservation laws, Journal of Scientific Computing, 75.1 (2018): 65-82.
16.
Xiaofeng Cai, Xiangxiong Zhang and Jianxian Qiu, Positivity-preserving high order finite volume HWENO schemes for compressible Euler equations, Journal of Scientific Computing, 68 (2016): 464-483.
Applications
Hongtao Liu, Mengyu Chen, Xiaofeng Cai, Yong Cao, Giovanni Lapenta, A combined immersed finite element and conservative semi-Lagrangian scheme for plasma-material interactions. Volume 488, 1 September 2023, 112232
Jiajie Chen, Xiaofeng Cai, Jianxian Qiu and Jing-Mei Qiu, Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for advection problem, Communications in Computational Physics, 30: 67-96, 2021.
Leitao Chen, Sauro Succi, Xiaofeng Cai, and Laura Schaefer, Semi-Lagrangian implicit Bhatnagar- Gross-Krook collision model for the finite-volume discrete Boltzmann method, Physical Review E, 101.6 (2020): 063301.
Hongtao Liu, Xiaofeng Cai, Giovanni Lapenta, Yong Cao, Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system, Communications in Nonlinear Science and Numerical Simulation, 102, 105941, 2021.
Leitao Chen, Laura Schaefer and Xiaofeng Cai, An Accurate Unstructured Finite Volume Discrete Boltzmann Method, ASME 2018 International Mechanical Engineering Congress and Exposition, Volume 7: Fluids Engineering: pp. V007T09A010.
Preprints
Nanyi Zheng, Xiaofeng Cai, Jing-Mei Qiu, Jianxian Qiu, Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations
Hongtao Liu, Xiaofeng Cai, Giovanni Lapenta, Yong Cao, Discrete unified gas kinetic scheme for the plasma flow in all electromagnetic plasma regimes.
学术兼职
中国数学会会员、美国《数学评论》评论员
Journal of Computational Physics, Computer Physics Communications, Journal of Scientific Computing, Communications in Computational Physics, International Journal for Numerical Methods in Fluids, Advances in Applied Mathematics and Mechanics, Results in Applied Mathematics, Computers and Mathematics with Applications等期刊审稿人
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