Some New Methods in Computational Fluid Dynamics

Author: Liu RuXun
Publisher:
Publish Date: 2004-03-01
Features: This book provides an in-depth introduction to the new developments in numerical methods for partial differential equations in the contemporary era, particularly focusing on the numerical methods for discontinuous or weak solutions that hold both theoretical significance and practical value, as well as the new challenges and issues we face. For example, in finite difference methods, Roe's Riemann solver method, Van Leer's MUSCL method, and Collela and Woodward's PPM method; high-resolution methods including TVD, TVB, ENO, and weighted ENO methods, etc.; finite volume methods, especially the unstructured grid finite volume methods for discontinuous solutions, as well as the generation of unstructured grids and the application of related software; several important and highly developed non-standard finite element methods: mixed elements, spatio-temporal elements, discontinuous finite elements, and moving mesh methods. Especially in today's numerical methods research abroad, in computational mechanics and computational physics topics, the very popular direction—numerical simulation methods for moving interface problems and reconstruction techniques for moving interfaces—this book discusses them quite comprehensively in China and conducts practical computational experiments. The purpose of this book is to introduce the new developments and new challenges in contemporary numerical methods for partial differential equations and computational fluid dynamics methods to researchers engaged in scientific and engineering computations, as well as senior undergraduate students and graduate students who have a basic knowledge of numerical methods and computational experience.