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

用于模拟和控制由扩散界面模型控制的变密度多相流的完全自适应和集成数值方法。

• 批准号: 238092916
• 负责人: Professor Dr. Michael Hintermüller
• 金额: --
• 依托单位: Forschungsgruppe Nichtglatte Variationsprobleme und Operatorgleichungen
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/238092916?language=en
• 关键词: Fully; adaptive; integrated; numerical; methods

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.

在这个项目中，我们(a)开发和分析了具有可变流体密度的多相流问题的数值模拟方法，这些方法保证了界面处局部过程的局部精细分辨率；(a)提出了扩散界面模型与表面偏微分方程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)为由扩散界面模型控制的多相流的最优控制制定稳健可靠的解决策略。我们工作的主要重点是(a)和（a’），其中(b)- (d)主题将随后根据(a), （a’）中取得的结果进行开发，并考虑到申请人在开发算法和离散化技术方面的专业知识，用于最优控制偏微分方程和变分不等式，包括CHNS系统。