**
数学与系统科学研究院
**

**
计算数学所学术报告**

**报告人：
汤
涛 研究员**

**
中国科学院计算数学所**

**香港浸会大学数学系**

**
**

**报告时间**： **2003年7月23日--25日,
下午3:00-5:00**

**报告地点**：**数学研究院院内
科技综合楼三层 311报告厅**

**报告摘要:**

We shall discuss the class of adaptive grid methods often called moving mesh methods

(or dynamic methods -- in contrast to the static methods) for solving time dependent PDEs.

These methods involve the solution of the underlying PDE for the physical problem solution

in conjunction with a so-called moving mesh PDE for the mesh itself.

In the first part of the talk, we will review the developments in the past two decades,

and will introduce a class of interpolation-free schemes.

In the second part of the talk, we will describe some recent developments on moving mesh

methods. In particular, we will discuss moving mesh schemes based on a fractional step

approach, which requires interpolation on the new grid.

In the third part of the talk, I will describe some applications of the moving mesh

methods for computational fluid dynamics. In the moving mesh procedure, we need to make

sure that the overall scheme preserves the relevant physical properties such as

divergence free for the incompressible flow and conservation of mass for hyperbolic

conservation laws. We will also discuss some preliminary results on the theoretical aspects

of the moving mesh approach.