中文摘要：

研究块结构自适应网格上计算任意界面上和任意区域内的数值积分方法,其中任意界面和任意区域通过一个水平集函数表示.首先介绍在一致网格上任意界面上和任意区域内的数值积分方法.然后,将该方法推广到块结构的自适应网格上.数值算例表明,自适应网格方法有二阶精度.同一致网格方法相比,自适应网格方法显著地减少了计算机存储量的需求.

英文摘要：

We study numerical integration over arbitrary interface and arbitrary domain on block-structured adaptive mesh. Arbitrary interface and arbitrary domain are described by a Level set function. We first describe numerical methods on uniform Cartesian grid. Then we extend the methods to block-structured adaptive mesh. Numerical calculations demonstrate that adaptive mesh methods are second-order accurate. Compared with uniform mesh methods, the adaptive mesh methods reduce needs on computer storage significantly.