We present a new discretization for advection-diffusion problems with Robin boundary conditions on complex time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme that uses a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the $L^1$, $L^2$, and $L^\infty$ norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to handle conversion of one concentration field to another across a moving boundary.

翻译：我们提出了一种新的分解方法,用于在复杂的时间依赖域内处理罗宾边界条件的分解问题,该方法基于Bochkov等人提出的将拉普尔操作员和罗宾边界条件分解的二级削减细胞数量限制方法,为克服小细胞问题,我们使用半拉格朗加方法处理分解方法。我们显示了用于分析测试问题和数字趋同研究的二级精度标准,即1美元、2美元和2美元。我们还展示了处理跨移动边界将一个集中场转换成另一个集中场的方法的能力。