Numerical computation of advection and diffusion on evolving diffuse interfaces
Numerical computation of advection and diffusion on evolving diffuse interfaces
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DOI：
10.1093/imanum/drq005
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发表时间：
2011-07-01
影响因子：
2.1
通讯作者：
Welford, Richard
中科院分区：
文献类型：
--
作者：
Elliott, Charles M.;Stinner, Bjoern;Welford, Richard
提出了一种计算运动表面输运和扩散的数值方法。该方法是基于一个扩散界面模型，其中体积扩散平流方程求解的一层上的厚度为100毫米的表面。体域中的守恒量是由密度加权的浓度，该密度在薄域的边界上为零。这种密度在双障碍物相场模型中自然出现。离散方程，然后制定一个移动的窄带上的网格点组成的固定网格。我们表明，离散方程是可解的离散窄带的演化受到自然约束。质量守恒，离散解满足稳定界。数值实验表明，该方法在空间上具有二阶精度。
We propose a numerical method for computing transport and diffusion on a moving surface. The approach is based on a diffuse interface model in which a bulk diffusion-advection equation is solved on a layer of thickness epsilon containing the surface. The conserved quantity in the bulk domain is the concentration weighted by a density which vanishes on the boundary of the thin domain. Such a density arises naturally in double obstacle phase field models. The discrete equations are then formulated on a moving narrow band consisting of grid points on a fixed mesh. We show that the discrete equations are solvable subject to a natural constraint on the evolution of the discrete narrow band. Mass is conserved and the discrete solution satisfies stability bounds. Numerical experiments indicate that the method is second-order accurate in space.