Control of Interface Evolution in Multiphase Fluid Flows
Control of Interface Evolution in Multiphase Fluid Flows
复制标题
多相流体流动中界面演化的控制
DOI：
10.1137/120896530
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Prohl
中科院分区：
文献类型：
--
作者：
L. Banas;M. Klein;A. Prohl
考虑二维多相流体问题中界面的最优控制问题。最小泛函由两部分组成：到给定密度分布的距离和界面长度。我们证明了周长泛函的相应相场近似的存在性，并导出了相应的一阶最优性必要条件。提出了一种基于低阶有限元的无条件稳定的全离散格式，并证明了相应的迭代收敛于离散参数为零的极限最优解。计算研究包括验证模型的相场近似、界面运动和拓扑变化，以及研究离散化、正则化误差以及泛函两部分之间的关系所产生的相对影响。
We consider an optimal control problem for the interface in a two-dimensional multiphase fluid problem. The minimization functional consists of two parts: the-distance to a given density profile and the interfacial length. We show existence and derive necessary first order optimality conditions for a corresponding phase-field approximation of the perimeter functional. An unconditionally stable fully discrete scheme which is based on low order finite elements is proposed, and convergence of corresponding iterates to solutions of the limiting optimality conditions for vanishing discretization parameters is shown. Computational studies are included to validate the model including the phase-field approximation, interface motion, and topological changes, as well as to study relative effects due to discretization, regularization errors, and the relation of both parts of the functional.
多相流体斯托克斯问题的最优控制
影响因子：
1.4
作者：
K. Kunisch;Xiliang Lu
通讯作者：
Xiliang Lu