A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries
Abstract
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.
Cite
@article{arxiv.2503.16877,
title = {A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries},
author = {Kaiyi Liang and Yuke Zhu and Jiyu Liu and Qinghai Zhang},
journal= {arXiv preprint arXiv:2503.16877},
year = {2025}
}