● 前言
綜述與進展
高精度加權緊致非線性格式的研究進展 (鄧小剛，劉昕，毛枚良，張涵信) 3
基於HDCS-E8T7格式的氣動噪聲數值模擬方法研究進展 (姜屹，鄧小剛，毛枚良，劉化勇) 14
計算流體力學中的驗證與確認 (鄧小剛，宗文剛，張來平，高樹椿，李超) 30
高精度格式及其構造理論
High-order accurate dissipative weighted compact nonlinear schemes (DENG Xiaogang) 43
Developing High-Order Weighted Compact Nonlinear Schemes (Xiaogang Deng，Hanxin Zhang) 58
Geometric conservation law and applications to high-order finite difference schemes with stationary grids (Xiaogang Deng，Meiliang Mao，Guohua Tu，Huayong Liu，Hanxin Zhang) 81
A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying Geometric conservation law (Xiaogang Deng，Yi Jiang，Meiliang Mao，Huayong Liu，Song Li，Guohua Tu) 97
Further studies on Geometric Conservation Law and applications to high-order finite difference schemeswith stationary grids (Xiaogang Deng，Yaobing Min，Meiliang Mao，Huayong Liu，Guohua Tu，Hanxin Zhang) 114
On the freestream preservation of finite volume method in curvilinear coordinates (Dan Xu，Xiaogang Deng，Yaming Chen，Yidao Dong，Guangxue Wang) 136 Reevaluation of high-order finite difference and finite volume algorithms with freestream preservation satisfied (Yidao Dong，Xiaogang Deng，Dan Xu，Guangxue Wang) 149
高精度格式推廣/應用技術研究
Extending Weighted Compact Nonlinear Schemes to Complex Grids with Characteristic-Based Interface Conditions (Xiaogang Deng，Meiliang Mao，Guohua Tu，Yifeng) 161
High-Order Behaviors of Weighted Compact Fifth-Order Nonlinear Schemes (Liu Xin，Deng Xiaogang，Mao Meiliang) 173
Large eddy simulation on curvilinear meshes using seventh-order dissipative compact scheme (Yi Jiang，Meiliang Mao，Xiaogang Deng，Huayong Liu) 178
Developing a hybrid flux function suitable for hypersonic flow simulation with high- order methods (Dongfang Wang，Xiaogang Deng，Guangxue Wang，Yidao Dong) 189
Efficiency benchmarking of seventh-order tri-diagonal weighted compact nonlinear scheme on curvilinear mesh (Shengye Wang，Xiaogang Deng，Guangxue Wang，Dan Xu，Dongfang Wang) 208
Developing a new mesh deformation technique based on support vector machine (Xiang Gao，Yidao Dong，Chuanfu Xu，Min Xiong，Zhenghua Wang and Xiaogang Deng) 228
Large eddy simulation on curvilinear meshes using seventh-order dissipative compact scheme (Yi Jiang，Meiliang Mao，Xiaogang Deng，Huayong Liu) 240
Effect of Nonuniform Grids on High-Order Finite Difference Method (Xu Dan，Deng Xiaogang，Chen Yaming，Wang Guangxue，Dong Yidao) 251
Extending Seventh-Order Dissipative Compact Scheme Satisfying Geometric Conservation Law to Large Eddy Simulation on Curvilinear Grids (Yi Jiang，Meiliang Mao，Xiaogang Deng and Huayong Liu) 274
Effect of Geometric Conservation Law on Improving Spatial Accuracy for Finite Difference Schemes on Two-Dimensional Nonsmooth Grids (Meiliang Mao，Huajun Zhu，Xiaogang Deng，Yaobing Min and Huayong Liu) 297
Further improvement of weighted compact nonlinear scheme using compact nonlinear interpolation (Zhen-Guo Yan，Huayong Liu，Yankai Ma，Meiliang Mao，Xiaogang Deng) 331
New nonlinear weights for improving accuracy and resolution of weighted compact nonlinear scheme (Zhenguo Yan，Huayong Liu，Meiliang Mao，Huajun Zhua，Xiaogang Deng) 342
Parallelizing a High-Order CFD Software for 3D，Multi-block，Structural Grids on the TianHe-1A Supercomputer (Chuanfu Xu，Xiaogang Deng，Lilun Zhang，Yi Jiang，Wei Cao，Jianbin Fang，Yonggang Che，Yongxian Wang，Wei Liu) 357 Collaborating CPU and GPU for large-scale high-order CFD simulations with complex grids on the TianHe-1A supercomputer (ChuanfuXu，XiaogangDeng，LilunZhang，etc) 371
Parallelizing and optimizing large-scale 3D multi-phase flow simulations on the Tianhe-2 supercomputer (Dali Li，Chuanfu Xu，Yongxian Wang，Zhifang Song，Min Xiong，Xiang Gao and Xiaogang Deng) 394
Performance modeling and optimization of parallel LU-SGS on many-core processors for 3D high-order CFD simulations (Dali Li，Chuanfu Xu，Bin Cheng，Min Xiong，Xiang Gao and Xiaogang Deng) 409
高精度格式的具體應用
High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems . (Xiaogang Deng，Meiliang Mao，Guohua Tu，Hanxin Zhang，Yifeng Zhang) 431
Numerical investigation on body-wake flow interaction over rod-airfoil configuration (Jiang Yi，Mao MeiLiang，Deng Xiaogang，Liu HuaYong) 453
Validation of a RANS transition model using a high-order weighted compact nonlinear scheme (TU GuoHua，Deng Xiaogang，MAO MeiLiang) 488
Osher Flux with Entropy Fix for Two-Dimensional Euler Equations (Huajun Zhu，Xiaogang Deng，Meiliang Mao，Huayong Liu and Guohua Tu) 495
基於雷諾應力模型的高精度分離渦模擬方法 (王聖業，王光學，董義道，鄧小剛) 518
鄧小剛院士及合作者發表的論文 535
內容簡介
本書選編了作者及研究團隊多年來在算法方面具有代表性的論文，主要涉及高精度有限差分格式構造方法及理論、高精度格式推廣及應用技術等內容。前言簡要介紹了作者本人以及所帶領的研究團隊開展研究工作的情況，靠前部分主要是作者在高精度有限差分算法研究方面的綜述性文章，第二部分為高精度格式及其構造理論，包括高精度有限差分格式的設計方法、頻譜分析方法以及幾何守恆律理論；第三部分為高精度格式推廣和應用技術研究，主要包括如何將標量方程下設計的高精度格式推廣到多維貼體坐標下的流動方程求解，如何在高性能計算機上進行高效並行計算等；第四部分為高精度格式的具體應用，主要介紹采用自主設計的HDCS格式和WCNS格式對典型復雜流動的精細模擬。附錄羅列了鄧小剛院士及合作者發表的部分論文。
