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最近我们在移动网格方面的研究在以下两个方面，一个是其在不可压流体计算中的应用，一个是其在双曲型守恒律上的应用。
My recent works on moving mesh method are focused on two problem: 1) its application to imcompressible flow; 2) its application to conservation law.

1. 不可压流体 (Application to Imcompressible Flow)

对于不可压流体，由于速度场满足不可压条件，所以奇异性相对较小，要构造控制函数比较困难。另外，将不可压的速度场从旧网格更新到新网格上，仍然要满足不可压条件是比较困难的。
For imcompressible, the singularity is comparatively weak bacause the velocity is divergence free that the mechanism to construct control function is much more difficult than those numerical examples we mentioned before. And to update the velocity to the new mesh efficiently but still divergence free is still a problem.

我们研究了对不可压流构造控制函数的方案，并且作为我们提出来的一般的网格间插值的公式，开发了一个新的旧网格到新网格插值的方案，使得不可压条件能够保持。下面是两个算例：
We studied the stragety to construct monitor function for imcompressible flow and give a general frame to update the solution to the new mesh, while at the same time keep certain constraint of the solution. The following are two numerical examples:

1. Double Shear Flow:

不可压Navier-Stokes方程
Imcompressible Navier-Stokes equation

在周期边界条件
with periodic boundary condition as

下，初值为
and initial value as

Mesh

Velocity

Contour of Vorticity

2. Boussinesq Flow:
方程为
The governing equation is as

2. 双曲型守恒律 (Application to Conservation Law)

我们主要考虑的是Euler方程
We here consider the Euler equation as

初值为
with initial value as