We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving boundaries, and introduce a cell-merging technique to overcome discontinuities caused by topological changes in cut cells and the small cell problem. We use a polynomial interpolation technique base on poised lattice generation to achieve fourth-order spatial discretization, and use a fourth-order implicit-explicit Runge-Kutta scheme for time integration. Numerical tests are performed on various moving regions, with advection velocity both matching and differing from boundary velocity, which demonstrate the fourth-order accuracy of the proposed method.

翻译：本文提出了一种在笛卡尔网格上求解移动边界二维对流扩散方程的四阶切割单元法。我们采用ARMS技术对移动边界进行显式精确表示，并引入单元合并技术以克服切割单元拓扑结构变化引起的不连续性及小单元问题。基于配置点阵生成的多项式插值技术被用于实现四阶空间离散，时间积分则采用四阶隐显式Runge-Kutta格式。通过对多种移动区域（其中对流速度与边界速度存在匹配与不匹配两种情况）进行数值测试，验证了所提方法具有四阶精度。