This book provides a concise and comprehensive introduction to several basic methods with more attention to their theoretical basis and applications in fluid dynamics. Furthermore, some new ideas are presented in this book, for example, a method to solve the transition matrix by difference operator transformation. For this method, the book gives the definition of Fourier integral transformation of translation operator, and proves the transition matrix equaling to the differential operator transformation, so that it is extended to general situations of explicit, implicit, multi-layer difference equations, etc. This flexible approach is also used in the differential part. In addition, the book also includes six types of equivalent stability definitions in two ways and deeply analyzes their errors, stabilities and convergences of the difference equations. What is more important, some new scientific contributions on lattice Boltzmann method (LBM) in recent years are presented in the book as well. The authors write the book combining their ten years teaching experience and research results and this book is intended for graduate students who are interested in the area of computational fluid dynamics (CFD). Authors list some new research achievements, such as simplified lattice Boltzmann method, the simplified lattice Boltzmann flux solver and discrete unified gas kinetic scheme, and expect that this new information could give readers possible further investigating ideas in their future research on CFD area.

Details the operator transformation method in difference methods which is a unique one Introduces several newly developing methods based on the Lattice Boltzmann Method in the second part of this book Helps readers master the general methods for exploring the basic laws of computational fluid dynamics

Autorentext
Prof. Guoxiang Hou received his B.Eng. and Ph.D. degrees in School of Naval Architecture and Ocean Engineering from Huazhong University of Science and Technology, Wuhan, China, in 1995 and 2000, respectively. He was engaged in postdoctoral research at the Electrical Engineering of Huazhong University of Science and Technology from 2000 to 2002. And from 2002 to 2005, Dr. Hou was engaged in the second postdoctoral research at the Institute of Hydrobiology, Chinese Academy of Sciences. In 2002, Dr. Hou was also employed as Associate Professor in the School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, and promoted as Professor since 2006. Prof. Hou has published more than 100 research papers in international journals and conferences. Prof. Caikan Chen received his B.Eng. degree in School of Aeronautics from Northwestern Polytechnical University, Xian, China, in 1966. Since then, he has been employed as Professor in the School of Naval Architecture and Ocean Engineering from Huazhong University of Science and Technology, Wuhan, China. He focuses on the finite difference methods at present. Shenglei Qin received his B.Eng. degree in School of Civil and Architectural Engineering from Hainan University, Haikou, China, in 2019. Now he is Ph.D. Student in School of Naval Architecture and Ocean Engineering from Huazhong University of Science and Technology, Wuhan, China. Mr. Qin focuses on the multiphase flows with the Lattice Boltzmann. Dr. Yuan Gao received his Ph.D. degree from Huazhong University of Science and Technology in June 2022. He studies the development and application of Simplified Lattice Boltzmann Methods. Dr. Kai Wang received his B.Eng. and Ph.D. degrees in School of Naval Architecture and Ocean Engineering from Huazhong University of Science and Technology in June 2013 and 2018, respectively. He focuses onthe research of drag reduction and the applications of Lattice Boltzmann Method.

Inhalt

1. Finite Difference Method.- 2. The Compatibility, Convergence and Stability of difference schemes.- 3. Common difference schemes for several model equations.- 4. Difference schemes for multi-dimensional problems.- 5 Variable coefficients and nonlinear problems.