Diffuse interface surface tension models in an expanding flow
Diffuse interface surface tension models in an expanding flow
复制标题
DOI：
10.4310/cms.2012.v10.n1.a16
复制
发表时间：
2012
影响因子：
1
通讯作者：
Wangyi Liu;A. Bertozzi;T. Kolokolnikov
中科院分区：
文献类型：
--
作者：
Wangyi Liu;A. Bertozzi;T. Kolokolnikov
考虑可压缩流中的扩散界面表面张力模型。感兴趣的方程是Cahn-Hilliard或Allen-Cahn方程，其中平流由非发散自由速度场产生。我们证明了这两个模型问题是适定的。我们特别感兴趣的是液滴破碎现象的解决方案的行为。一维、二维和三维的数值模拟结果均表明，Cahn-Hilliard模型对液滴破碎更为有效。使用渐近方法，我们正确地预测的崩溃条件的Cahn-Hilliard模型。此外，我们还证明了Allen-Cahn模型在一定条件下不会由于极大值原理而破裂。
We consider a di usive interface surface tension model under compressible ow. The equation of interest is the Cahn-Hilliard or Allen-Cahn equation with advection by a non-divergence free velocity eld. We prove that both model problems are well-posed. We are especially interested in the behavior of solutions with respect to droplet breakup phenomena. Numerical simulations of 1,2 and 3D all illustrate that the Cahn-Hilliard model is much more e ective for droplet breakup. Using asymptotic methods we correctly predict the breakup condition for the Cahn-Hilliard model. Moreover, we prove that the Allen-Cahn model will not break up under certain circumstances due to a maximum principle.