长期致力于计算流体力学先进算法及应用和空气动力学基础问题的研究。主要成果有：（1）在结构网格高精度计算方法方面，提出了基于特征分解的高精度高分辨率紧致－WENO 混合格式和色散耗散分别优化的MDCD格式；提出了有效消除Godunov类型激波捕捉格式激波附近不稳定的旋转黎曼求解器；（2）在非结构网格高精度计算方法方面，提出了非结构网格高精度有限体积方法和DG方法的高效、保精度限制器以及紧致模板高精度有限体积重构方法；(3)在不可压缩NS方程数值计算方法方面， 提出了“连续投影方法”的概念，通过严格的截断误差分析，得到了投影方法速度、压力为完全二阶精度和三节精度的充分条件，并构造了相应的二阶和三阶投影格式；（4）提出了计算飞行器动导数的敏感性参数方法，解决了飞行器动导数理论和计算的关键问题；（5）开发了模拟高超声速复杂非定常流动的计算程序，并应用于飞行器气动力、热预测和湍流边界层减阻控制;(6) 发展了压气机和涡轮多级非定常流动的计算软件和非定常损失分析方法，可用于多级压气机和涡轮三维动静叶干涉、时许效应等的数值模拟，还可以定量分析非定常流动损失的大小和分布。
在人才培养方面，指导的博士毕业生刘淼儿获我校优秀博士论文二等奖；博士毕业生李万爱获我校优秀博士论文一等奖，他的博士论文的英文版在Springer出版社的Springer Theses 丛书出版（我校首批四篇论文之一）；委托培养的博士生孙振生（在清华完成全部培养环节）获得全军优秀博士论文奖。
主要论文如下。
[1] Pan J, Ren Y, Sun Y. High order sub-cell finite volume schemes for solving hyperbolic conservation laws II: Extension to two-dimensional systems on unstructured grids[J]. Journal of Computational Physics, 2017, 338: 165-198.
[2] Pan J, REN Y. High order sub-cell finite volume schemes for solving hyperbolic conservation laws I: basic formulation and one-dimensional analysis[J]. SCIENCE CHINA Physics, Mechanics & Astronomy, 2017
[3] Zhu Y, Sun Z, Ren YX, et al. A Numerical Strategy for Freestream Preservation of the High Order Weighted Essentially Non-oscillatory Schemes on Stationary Curvilinear Grids[J]. Journal of Scientific Computing, 2017, 1-28.
[4] Chen Z, Huang X, Ren YX, et al. General Procedure for Riemann Solver to Eliminate Carbuncle and Shock Instability[J]. AIAA Journal, 2017: 1-15.
[5] Wang Q, Ren Y X, Pan J, et al. Compact high order finite volume method on unstructured grids III: Variational reconstruction[J]. Journal of Computational Physics, 2017, 337: 1-26.
[6] Wang Q, Ren YX, Li W, Compact high order finite volume method on unstructured grids II: Extension to two-dimensional Euler equations[J]. Journal of Computational Physics, 2016, 314: 883-908
[7] Wang Q, Ren YX, Li W, Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes[J]. Journal of Computational Physics, 2016, 314: 863-882.
[8] Sun Y, Yu M, Jia Z, Ren YX, A cell-centered Lagrangian method based on local evolution Galerkin scheme for two-dimensional compressible flows[J]. Computers & Fluids, 2016, 128: 65-76.
[9] Sun Z, Ren YX, Zha B, et al. High Order Boundary Conditions for High Order Finite Difference Schemes on Curvilinear Coordinates Solving Compressible Flows[J]. Journal of Scientific Computing, 2015, 65(2): 790-820.
[10] Wang Q, Ren YX, An accurate and robust finite volume scheme based on the spline interpolation for solving the Euler and Navier–Stokes equations on non-uniform curvilinear grids[J]. Journal of Computational Physics, 2015, 284: 648-667.
[11] Sun Z, Ren YX, A sixth order hybrid finite difference scheme based on the minimized dispersion and controllable dissipation technique[J]. Journal of Computational Physics, 2014, 270:238–254.
[12] Li W, Ren YX, The multi-dimensional limiters for discontinuous Galerkin method on unstructured grids[J]. Computers & Fluids, 2014, 96(11):368–376.
[13] Wang Q, Ren YX, Sun Z, et al. Low dispersion finite volume scheme based on reconstruction with minimized dispersion and controllable dissipation[J]. Science China Physics, Mechanics and Astronomy, 2013, 56(2):423-431.
[14] Li W, Ren YX. High-order k -exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids[J]. International Journal for Numerical Methods in Fluids, 2012, 70(6):742–763.
[15] Li W, Ren YX, The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids II: Extension to high order finite volume schemes[J]. Journal of Computational Physics, 2012, 231(11):4053–4077.
[16] Li W, Ren YX, Lei G, et al. The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids.[J]. Journal of Computational Physics, 2011, 230(21):7775–7795.
[17] Sun Z, Ren YX, Zhang S, et al. High-resolution finite difference schemes using curvilinear coordinate grids for DNS of compressible turbulent flow over wavy walls[J]. Computers & Fluids, 2011, 45(1):84–91.
[18] Sun Z, Ren YX, Larricq C, et al. A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence[J]. Journal of Computational Physics, 2011, 230(12):4616–4635.
[19] Lei GD, Ren YX, Computation of the stability derivatives via CFD and the sensitivity equations[J]. Acta Mechanica Sinica, 2011, 27(2): 179-188.
[20] Sun Z, Ren YX, Larricq C. Drag reduction of compressible wall turbulence with active dimples[J]. Science China(Physics, 2011, 54(2):329-337.
[21] Sun Y, Ren YX, The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws[J]. Journal of Computational Physics, 2009, 228(13):4945–4960.
[22] Ren YX, Evaluation of the Stability Derivatives Using the Sensitivity Equations[J]. AIAA Journal, 2008.
[23] Ren YX, Liu M, Zhang H. Implementation of the divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the collocated grids[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2007, 2(4):746-759.
[24] Ren YX, Sun Y. A multi-dimensional upwind scheme for solving Euler and Navier–Stokes equations[J]. Journal of Computational Physics, 2006, 219(1):391–403.
[25] Tan, LH, Ren, YX, Wu ZN. Analytical and numerical study of the near flow field and shape of the Mach stem in steady flows [J]. Journal of Fluid Mechanics, 2006, 54:341-362.
[26] Ren YX, Tan LH, Gao B, Wu ZN. On the characteristics of the Mach stem [J]. Journal of Fluid Mechanics, 2005, 19(28-29):1511-1514.
[27] Ren YX, Jiang Y, Liu M, et al. A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations[J]. Acta Mechanica Sinica, 2005, 21(6):542-549.
[28] Liu M, Ren YX, Zhang H, A class of fully second order accurate projection methods for solving the incompressible Navier–Stokes equations[J]. Journal of Computational Physics, 2004, 200(1):325–346.
[29] Ren YX, Liu M, Zhang H, A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws[J]. Journal of Computational Physics, 2003, 192(2):365–386.
[30] Ren YX, A robust shock-capturing scheme based on rotated Riemann solvers[J]. Computers & Fluids, 2003, 32(10):1379–1403.
