Adaptive Higher-Order Variational Methods for Aerodynamic Applications in Industry, 欧盟第六框架特别研究项目，2006.9-2009.8，中方负责人。对流占优问题的高精度数值方法研究与应用, 国家自然科学基金, 2007.01-2009.12，负责人。双曲守恒律初值问题的间断Galerkin有限元方法研究, 留学回国人员科研启动基金，独立。对流占优问题的数值方法研究， 南京大学人才引进启动基金，独立。非均匀介质中溶质运移模型的多尺度分析与计算，江苏省创新人才（学术）基金，2006.06-2009.05, 参与。溃坝、涌浪等畸变自由面问题的数值模拟方法研究， 国家自然科学基金 2004.01-2006.12，参与。Publications in Refereed Journals(Impact Factor, J. Comput. Phys. 2.372; SIAM J. Sci. Comput. 1.784; Commun. Comput. Phys. 1.633; Comput. Methods Appl. Mech. Engrg. 1.488; Computers & Fluids 1.431; J. Sci. Comput. 1.293; J. Comput. Appl. Math. 0.943;Int. J. Numer. Methods Fluids, 0.712; J. Comput. Math.0.667, Sci. China Ser. A-Math, 0.371)J. Zhu and J. Qiu: A Class of Forth order Finite Volume Hermite Weighted Essentially Non-oscillatory Schemes, Science in China, Series A--Mathematics, 51 (2008), 1549-1560.C. Lu, J. Qiu and R. Wang: Weighted Essential Non-oscillatory Schemes for Tidal Bore on Unstructured Meshes, International Journal for Numerical Methods in Fluids, to appear.J. Qiu: Development and comparison of numerical fluxes for LWDG methods, Numerical Mathematics: Theory,Methods and Applications, 1 (2008), 435-459.J. Zhu, J. Qiu, C.-W. Shu and M. Dumbser: Runge-Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes, J. Comput. Phys., 227 (2008) 4330–4353.J. Qiu, T. G. Liu and B. C. Khoo: Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method, Commun. Comput. Phys., 3 (2008), 479-504.H. S. Dou, H. M. Tsai, B. C. Khoo and J.Qiu: Simulations of detonation wave propagation in rectangular ducts using a three-dimensional WENO scheme, Combustion and Flame 154 (2008) 644–659.J. Qiu, T. G. Liu and B. C. Khoo: Runge-Kutta Discontinuous Galerkin methods for compressible two-medium flow simulations: one-dimensional case, J. Comput. Phys., 222(2007), 353-373.J. Qiu: A Numerical comparison of the Lax-Wendroff Discontinuous Galerkin Method Based on Different Numerical Fluxes, J. Sci. Comput., 30(2007), 345-367.J. Qiu: Hermite WENO Schemes with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi equations, J. Comp. Math., 25(2007), 131-144.J. Qiu: WENO Schemes with Lax-Wendroff Type Time Discretizations for Hamilton-Jacobi equations, J. Comput. Appl. Math., 200(2007), 591-605.J. Qiu, B.C. Khoo and C.-W. Shu: A Numerical Study for the Performance of the Runge-Kutta Discontinuous Galerkin Method Based on Different Numerical Fluxes, J. Comput. Phys., 212 (2006), 540-565.J. Qiu and C.-W. Shu: A comparison of trouble cell indicators for Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput.，27 (2005), 995-1013.J. Qiu and C.-W. Shu: Runge-Kutta discontinuous Galerkin method using WENO limiters，SIAM J. Sci. Comput. , 26（2005），907-929.J. Qiu and C.-W. Shu: Herimte WENO scheme for Hamilton-Jacobi equations. J. Comput. Phys., 204(2005), 82-99.J. Qiu, M. Dumbser and C.-W. Shu: The discontinuous Galerkin method with Lax-Wendroff type time discretizations, Comput. Methods Appl. Mech. Engrg., 194 (2005),4528-4543.J. Qiu and C.-W. Shu: Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method (II): two dimensional case, Computers & Fluids , 34 (2005) 642-663.J. Qiu and C.-W. Shu: Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one dimensional case, J. Comput. Phys., 193 (2004) 115-135.J. Qiu and C.-W. Shu: Finite difference WENO schemes with Lax-Wendroff type time discretizations. SIAM J. Sci. Comput. 24 (2003) 2185-2198.J. Qiu and C.-W. Shu: On the construction, comparison, and local characteristic decomposition for high order central WENO schemes. J. Comput. Phys., 183 (2002) 187-209.Z. Xu, J. Qiu and R. Liu: Some optimal methods for WENO scheme in hyperbolic conservation laws, J. of Univ. Sci. Tech. China, 23 (2004), 29-37, (in Chinese).Z.Xu, R. Liu and J. Qiu: Advances in weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advances of Mechanics, 34(2004) pp. 9-22, (in Chinese).R. Wang, J. Qiu, J. Dai and N. Zhao: A high resolution Gauss scheme with staggered grid for shallow water equation, Advances in Water Science, 13 (2002),403-408, (in Chinese).C. Wang, J. Qiu and J. Dai: Construction and numerical simulation of high accuracy weighted ENO schemes, Chinese J. Comput. Phys., 18 (2001), 381-384, (in Chinese).J. Qiu and J. Dai: A Class of Gauss schemes with staggered grids in two dimensions, Chinese J. of Comput. Phys., 18 (2001), 241-246, (in Chinese).J. Qiu, J. Dai, N. Zhao and R. Wang: A Class of Gauss schemes with staggered grids, Mathematica Applicata, 14-2 (2001) , 1-5, (in Chinese).J. Qiu and J. Dai: A class of difference schemes with staggered grids for Hamilton-Jacobi equations, J. Nanjing Univ. Aero. Astro., 32 (2000), 573-578, (in Chinese).J. Qiu and K. You: A class of generalization Lax-Friedrichs schemes, J. Jimei Univ., No. 3, (1998), (in Chinese).J. Qiu and K. You: Gauss scheme for numerical 0rdinary differential equation, J. Jimei Univ.,No. 4, (1997), (in Chinese).J. Qiu: A class of large tine step TVD schemes , J. Jimei Univ., No. 1, (1995), (in Chinese).J. Qiu: Convergence of the secondorder large time step EO scheme ,J. Jimei Univ., No. 2, (1994), (in Chinese).J. Qiu: A class generalization large time step up-wind scheme , J. Jimei Univ.,No. 1, (1992), (in Chinese).--------------------------------------------------------------------------------Publications in Conference Proceedings and books· J. Qiu, T. G. Liu and B. C. Khoo: Runge-Kutta discontinuous Galerkin methods for simulations of multi-phase flow , Scientific Computational PDEs, Dec. 12-16, 2005,Hong Kong. (Invited speaker in MS-6).· J. Qiu, B. C. Khoo and C.-W. Shu: A numerical study of RKDG methods with different numerical fluxes, The International Workshop on Computational Science and its Education, Aug. 29-Sept 2,2005, Beijing, China. (Invited speaker).· J. Qiu, T. G. Liu and B. C. Khoo, Simulations of multi-phase flow using Runge-Kutta discontinuous Galerkin methods with conservative approach of interfaces, Asian Mathematical Conference, July 20-23, 2005, Singapore. (Contribution speaker).· J. Qiu and C.-W. Shu, WENO limiters for Runge-Kutta discontinuous Galerkin methods, International Conference on Scientific Computing, June 4-8, 2005, Nanjing. (Invited speaker and organizer).· J. Qiu and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods with WENO type limiters, First Singapore Workshop on Differential Equations and Scientific Computing, Dec. 23-24, 2004, Singapore. (Invited speaker).· J. Qiu and C.-W. Shu, RKDG methods with WENO type limiter for conservation laws, Proc. of the Sixth World Congress on Computational Mechanics, pp. 203. 2004,Beijing, P.R. China. @2004 Tsinghua University Press & Springer-Verlag. (Invited speaker in MS-26).· J. Qiu, Ning Zhao, Jiazun Dai and Ruyun Wang, A class of large time-step MUSCL schemes, Proc. of the 4th Asian Computational Fluid Dynamics Conference, pp. 536-540,2000, Sichuan, P.R. China. (Contribution speaker).· J. Dai and J. Qiu, Numerical methods for differential equations, Southeastern University Press, 2002.--------------------------------------------------------------------------------Preprints:C. Lu, J. Qiu and R. Wang: A numerical study for the performance of the WENO schemes based on different numerical fluxes for the shallow water equations, submitted to J. Comp. Math..H. Zhu and J. Qiu: Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: one dimensional case, submitted to J. Comput. Phys.J. Zhu and J. Qiu: Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method III: Unstructured meshes, submitted to J. Sci. Comput.
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