@Article{CiCP-22-1413,
author = {Yongbo Deng, Zhenyu Liu and Yihui Wu},
title = {Topology Optimization of Capillary, Two-Phase Flow Problems},
journal = {Communications in Computational Physics},
year = {2017},
volume = {22},
number = {5},
pages = {1413--1438},
abstract = {<p style="text-align: justify;">This paper presents topology optimization of capillary, the typical two-phase
flow with immiscible fluids, where the level set method and diffuse-interface model
are combined to implement the proposed method. The two-phase flow is described by
the diffuse-interface model with essential no slip condition imposed on the wall, where
the singularity at the contact line is regularized by the molecular diffusion at the interface
between two immiscible fluids. The level set method is utilized to express the
fluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface.
Based on the variational procedure for the total free energy of two-phase flow, the
Cahn-Hilliard equations for the diffuse-interface model are modified for the two-phase
flow with implicit boundary expressed by the level set method. Then the topology optimization
problem for the two-phase flow is constructed for the cost functional with
general formulation. The sensitivity analysis is implemented by using the continuous
adjoint method. The level set function is evolved by solving the Hamilton-Jacobian
equation, and numerical test is carried out for capillary to demonstrate the robustness
of the proposed topology optimization method. It is straightforward to extend this
proposed method into the other two-phase flows with two immiscible fluids.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0003},
url = {http://global-sci.org/intro/article_detail/cicp/10448.html}
}