Barrett Aaron, Fogelson Aaron L, Griffith Boyce E
Department of Mathematics, University of Utah, Salt Lake City, UT, USA.
Departments of Mathematics and Bioengineering, University of Utah, Salt Lake City, UT, USA.
J Comput Phys. 2022 Jan 15;449. doi: 10.1016/j.jcp.2021.110805. Epub 2021 Oct 28.
We present a new discretization approach to 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. [8] to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme along with a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the , , and norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to convert one chemical species to another across a moving boundary.
我们提出了一种新的离散化方法，用于处理复杂的、随时间变化的区域上具有罗宾边界条件的对流扩散问题。该方法基于Bochkov等人[8]引入的二阶切割单元有限体积法，用于离散拉普拉斯算子和罗宾边界条件。为了克服小单元问题，我们使用了一种分裂格式以及半拉格朗日方法来处理对流。我们在解析测试问题和数值收敛性研究中，分别在 、 和 范数下证明了二阶精度。我们还展示了该格式在移动边界上实现一种化学物质向另一种化学物质转化的能力。
