Numerical simulation methods and moving interface tracking

Author: Liu RuXun, Wang ZhiFeng (editors)
Publisher:
Publish Date: 2001-10-01
Features: The primary goal of this course is not to conduct research and application on motion interface tracking methods, but rather to use this issue as a thread to integrate the discussion of mathematical models, numerical methods, especially the introduction and teaching of effective methods developed in recent years, under the same objective. Therefore, the basic content of this course can be divided into three parts:
1. Introducing students to some meaningful and interesting mathematical models of motion interface problems. These include both classic Stefan problems or moving boundary problems, free surface problems, and composite models of basic physical fields of moving interfaces, which are currently more challenging. We hope readers can see their practical physical significance and application prospects, thereby generating interest and a desire to solve them.
2. Introducing and teaching contemporary numerical methods. This includes high-resolution methods and reconstruction methods for solving motion interface tracking, as well as numerical methods for simulating basic physical fields, especially how to coordinate motion interface tracking calculations with main field numerical simulations. Here, it is natural to teach the fundamental theory and design methods of finite difference methods; particularly the concepts and ideas of Upwind or characteristic lines, as well as the theory and methods of weak or discontinuous solutions, such as Riemann problems, Roe's methods, and various important high-resolution methods, etc. Additionally, a brief yet practical introduction will be provided on discontinuous finite element methods and finite volume methods.
3. Using the numerical methods and programs introduced, to perform actual calculations and simulations of typical motion interface mathematical models. This means another important content of this book is to apply the taught numerical methods to typical motion interface problems for numerical simulation experiments, comparison, analysis, and evaluation. From this, the characteristics, adaptability, existing issues, and points to note of various numerical methods will be explained.