本书选编了作者及研究团队多年来在算法方面具有代表性的论文，主要涉及高精度有限差分格式构造方法及理论、高精度格式推广及应用技术等内容。前言简要介绍了作者本人以及所带领的研究团队开展研究工作的情况，靠前部分主要是作者在高精度有限差分算法研究方面的综述性文章，第二部分为高精度格式及其构造理论，包括高精度有限差分格式的设计方法、频谱分析方法以及几何守恒律理论；第三部分为高精度格式推广和应用技术研究，主要包括如何将标量方程下设计的高精度格式推广到多维贴体坐标下的流动方程求解，如何在高性能计算机上进行高效并行计算等；第四部分为高精度格式的具体应用，主要介绍采用自主设计的HDCS格式和WCNS格式对典型复杂流动的精细模拟。附录罗列了邓小刚院士及合作者发表的部分论文。
前言
综述与进展
高精度加权紧致非线性格式的研究进展 (邓小刚，刘昕，毛枚良，张涵信) 3
基于HDCS-E8T7格式的气动噪声数值模拟方法研究进展 (姜屹，邓小刚，毛枚良，刘化勇) 14
计算流体力学中的验证与确认 (邓小刚，宗文刚，张来平，高树椿，李超) 30
高精度格式及其构造理论
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
高精度格式推广/应用技术研究
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，
