论文标题
二阶准确的半拉格朗日方法，用于对流 - 扩散方程，界面跳跃
A second-order accurate semi-Lagrangian method for convection-diffusion equations with interfacial jumps
论文作者
论文摘要
在本文中，我们提出了一种二阶精确有限差异方法，用于在移动界面上使用界面跳跃来求解对流散文方程。所提出的方法是在半拉格朗日框架下构建的，用于对流扩散方程；在跳跃条件下，开发了一种新型的插值方案。结合二阶幽灵流体方法[3]，一种锋利的捕获方法，在接口附近具有一阶局部截断误差，而从接口方面开发了远离接口的二阶截断误差。另外，当速度梯度在界面上跳跃时，会提出级别的对流算法。数值实验支持以下结论：对流扩散方程和级别对流的提议的方法对于二阶收敛解决方案和界面位置是必需的。
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.
