A second-order accurate semi-Lagrangian method for convection-diffusion equations with interfacial jumps
Abstract
In this paper, we present a second-order accurate finite-difference method for solving convectiondiffusion equations with interfacial jumps on a moving interface. The proposed method is constructed under a semi-Lagrangian framework for convection-diffusion equations; a novel interpolation scheme is developed in the presence of jump conditions. Combined with a second-order ghost fluid method [3], a sharp capturing method with a first-order local truncation error near the interface and second-order truncation error away from the interface is developed for the convectiondiffusion equation. In addition, a level-set advection algorithm is presented when the velocity gradient jumps across the interface. Numerical experiments support the conclusion that the proposed methods for convection-diffusion equations and level-set advection are necessary for the second-order convergence solution and the interface position.
Cite
@article{arxiv.2005.13717,
title = {A second-order accurate semi-Lagrangian method for convection-diffusion equations with interfacial jumps},
author = {Hyuntae Cho and Yesom Park and Myungjoo Kang},
journal= {arXiv preprint arXiv:2005.13717},
year = {2020}
}