[8] 分数阶对流扩散方程的格子Boltzmann方法研究（No.11602057，主持），2017/01-2019/12，国家自然科学基金青年项目；

[7] 求解刚性及非线性随机延迟微分方程的数值方法（No.11671083，排3），2017/01-2020/12，国家自然科学基金面上项目；

[6] 空间分数阶扩散问题的LB方法研究（No.2014M551483，主持），2015/01-2016/12，中国博士后基金项目；

[5] 基于电磁场传播的特征值问题的计算及应用研究（No.11471074，排5），2015/01-2018/12，国家自然科学基金面上项目；

[4] 空间分数阶偏微分方程高精度快速算法的研究（No.11271068，排4），2013/01-2016/12，国家自然科学基金面上项目；

[3] 微尺度气体流动格子Boltzmann 方法的复杂边界研究（No.11026181，主持），2011/01-2011/12，国家自然科学基金天元项目；

[2] 分数阶偏微分方程初边值问题差分方法研究（No.10871044，排3），2009/01-2011/12，国家自然科学基金面上项目；

[1] 军工（No. 6950232074, 6950232077，排3），2009/01-2010/12，国家重大科技专项项目。

• 发表的学术论文：
• [25] Xianzhong Yan, Yonglong Ye,  Jun Chen, Xiaofeng Wang and Rui Du*, Improved multiple-relaxation-time lattice Boltzmann model for Allen–Cahn equation, International Journal of Modern Physics C, 2021, DOI:10.1142/S0129183121500868
• [24] Rui. Du*, Yibo Wang, Lattice BGK model for time-fractional incompressible Navier-Stokes equations Applied Mathematics Letter, 2021, 114:106911.
• [23] Zhaopeng Hao, Zhongqiang Zhang, Rui Du*, Fractional centered difference scheme for high-dimensional integral fractional Laplacian, Journal of Computational Physics, 2021, 424:109851.
• [22] Hong Liang∗, Chunhua Zhang, Rui Du, Yikun Wei, Lattice Boltzmann method for fractional Cahn-Hilliard equationCommun Nonlinear Sci Numer Simulat, 2020, 91:105443.
• [21] R. Du, P. Gokulavani, M.Muthtamilselvan* et. al, Influence of the Lorentz force on the ventilation cavity having a centrally placed heated baffle filled with the Cu − Al2O3 − H2Ohybrid nanofluid, International Communications in Heat and Mass Transfer, 2020, 116:104676.
• [20] R. Du, J.C. Wang, D.K. Sun*, Lattice-Boltzmann Simulations of the Convection-Diffusion Equation with Different Reactive Boundary Conditions, Mathematics, 2020, 8(1):13.
• [19] R. Du*, Z.X. Liu, A lattice Boltzmann model for the fractional advection-diffusion equation coupled with incompressible Navier-Stokes equation, Applied Mathematics Letter, 2020, 101:106074.
• [18] Z.H. Chai, H. Liang, R. Du, B.C. Shi*, A lattice Boltzmann model for two-phase flow in porous media, SIAM J. Sci. Comput. 2019, 41(4): B746-B772. (ESI 高被引论文)
• [17] Hong Sun, Zhi-zhong Sun, Rui Du*，A linearized second-order difference scheme for the nonlinear time-fractional fourth-order reaction-diffusion equation，Numer. Math. Theor. Meth. Appl., 2019, 12:1168-1190.
• [16] R. Du, D.K. Sun, B.C. Shi, Z.H. Chai*, Lattice Boltzmann model for time sub-diffusion equation in Caputo sense, Applied Mathematics and Computation, 2019, 358:80-90.
• [15] Jin-ye Shen, Zhi-zhong Sun*, Rui Du, Fast finite difference schemes for the time-fractional diffusion equation with a weak singularityat the initial time, Asian Journal of Applied Mathematics, East Asian Journal on Applied Mathematics，2018, 8(4): 834-858.
• [14] Cui-cui Ji, Rui Du, Zhizhong Sun*，Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives, International Journal of Computer Mathematics,  2018, 95(1), 255-277.
• [13] Rui Du*， Zhao-peng Hao， Zhi-zhong Sun, Lubich's second-order methods for the distributed-order time-fractional differential equations with smooth solutions, East Asian Journal on Applied Mathematics, 2016,6(2):131-151.
• [12] Rui Du*, Zhizhong Sun, Guanghua Gao, A second-order linearized three-level backward Euler scheme for a class of nonlinear expitaxial growth model, Int. J. Comput. Math., 2015, 92(11):2290-2309.
• [11] Hong Sun, Rui Du, Weizhong Dai, Zhizhong Sun*, A high order accurate numerical method for solving two-dimensional dual-phase-lagging equation with temperature jump boundary condition in nano heat conduction，Numerical Methods for Partial Differential Equations, 2015, 31:1742-1768.
• [10] Rui Du*, Wenwen Liu, A New Multiple-relaxation-time Lattice Boltzmann Method for Natural Convection,Journal of Scientific Computing, 2013, 56(1):122-130.
• [9] Sheng Chen*, Rui Du, Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity, Energy, 2011, 36:1721-1734.
• [8]R. Du*, W. R. Cao, Z. Z. Sun, A compact difference scheme for  the fractional diffusion-wave equation, Applied Mathematical Modeling, 2010,34:2998-3007.
• [7] Rui Du, Baochang Shi*, Incompressible Multi-relaxation-time Lattice Boltzmann Model in 3d Space, Journal of Hydrodynamics, 2010, 22(6):782-787.
• [6] Rui Du，Baochang Shi*, Incompressible MRT lattice Boltzmann model with eight velocities in 2D space,International Journal of Modern Physics C, 2009, 20:1023-1037.
• [5]Rui Du, Baochang Shi*, The lattice Boltzmann method for the thermocapillary flow in a cavity under microgravity condition, Computers and Mathematics with Applications, 2008, 55:1433-1440.
• [4] Rui Du, Baochang Shi*, A novel scheme for forcing term in the lattice BGK model, International Journal of Modern Physics C, 2006, 17:945-958.
• [3] Rui Du, Baochang Shi* and Xingwang Chen, Multi-relaxation-time lattice Boltzmann model for incompressible flow,      Physics Letters A, 2006, 359:564-572.
• [2] 杜睿, 施保昌，格子Boltzmann 方法中的曲边界处理，计算物理，23 (2006), 405-411.
• [1] Rui Du，Baochang Shi* et al, An implicit scheme for incompressible LBGK model, J. Hydrodynamic, Part B. 17 (2005), 330-337. (EI)