Fully adaptive and integrated numerical methods for the simulation and control of variable density multiphase flows governed by diffuse interface models.

在本项目中，我们(A)开发和分析具有可变流体密度的多相流问题的数值模拟方法，以保证界面局部过程的局部精细分辨率；(a‘)提出用于扩散界面模型和表面偏微分方程组(PDE)耦合的自适应离散化概念；(B)开发、实施和分析由扩散界面模型控制的多相流的模型预测反馈控制策略；(C)制定和分析多相流的最优控制问题；(D)为受扩散界面模型控制的多相流的最优控制开发稳健和可靠的解决策略。我们工作的主要重点是(A)和(a‘)，其中专题(B)--(D)将在(A)、(a’)所取得的成果的基础上随后发展，并考虑到申请人在开发包括CHNS系统在内的偏微分方程和变分不等的最优控制的算法和离散化技术方面的专门知识。

In this project we (a) develop and analyse numerical methods for the simulation of multiphase flow problems with variable fluid densities which guarantee a locally refined resolution of the local processes at the interface; (a') propose adaptive discretization concepts for the coupling of diffuse interface models and surface partial differential equations (PDEs); (b) develop, implement and analyze model-predictive feedback control strategies for multiphase flows governed by diffuse interface models; (c) formulate and analyze optimal control problems for multiphase flows; (d) develop robust and reliable solution strategies for optimal control of multiphase flows governed by diffuse interface models. The primary focus of our work is on (a) and (a'), where as the topics (b)--(d) are to be developed subsequently based on the results achieved in (a), (a') and given the expertise of the applicants in the development of algorithms and discretization techniques for optimal control of partial differential equations and variational inequalities including the CHNS system.