High performance numerical methods for moving interface problems and uncertainty analysis

数值方法和计算技术在大学和工业中几乎所有的科学研究中起着重要的作用。在许多领域，计算机模拟已经补充甚至取代了实验。大多数工程科学以力学原理为基础，计算力学工具在工程实践中经常使用；比如飞机和推进系统的设计，大坝和桥梁的设计。申请人在巴黎高等技术学院领导一个研究小组，开发计算方法和相应的软件来解决各种复杂的工程问题，例如大坝溃坝淹没引起的流量或柔性飞机机翼周围的流量。提出的研究计划涉及发展先进的数值方法和软件，以准确有效地解决存在移动界面的流动和固体问题，例如分离液体和空气相的界面（如在自然自由表面流动或在润滑气动系统中），或混凝土大坝中的裂纹扩展。当结构被流包围时，也会出现移动界面问题。随着计算方法和计算机在解决大量确定性问题方面变得越来越强大，人们对开发量化工程预测中的不确定性的方法越来越感兴趣。本提案的另一个主题是发展分析由不确定数据引起的数值模型中的不确定性传播的技术。然后，这些数据可以用于执行敏感性和可靠性分析，以帮助做出更好的基于风险的决策。

Numerical methods and computing technologies play an important part of almost all scientific research at universities and in industry. In many areas, computer simulations have complemented or even replaced experiments. Most engineering science is based on the principles of mechanics, and computational mechanics tools are routinely used in engineering practice; such us for the design of aircraft and propulsion systems or for the design of dams and bridges. The applicant heads a research group at the Ecole de technologie superieure that develops computational methods and their corresponding software to solve various complex engineering problems, such as flows resulting from a dam break inundation or a flow around a flexible aircraft wing. The proposed research program concerns the development of advanced numerical methods and software to accurately and efficiently solve flow and solid problems where there is a moving interface, such as an interface separating the liquid and air phases (as in natural free-surface flows or in a lubrication aero-system), or a crack propagating in a concrete dam. Moving interface problems also occur when a structure is surrounded by a flow. As computational methods and computers become more powerful to solve a large class of deterministic problems there is increasing interest in developing methods to quantify uncertainties in engineering predictions. Another topic of this proposal is the development of techniques to analyze uncertainty propagation in numerical models caused by uncertain data. These could then be used to perform sensitivity and reliability analyses to help make better risk-based decisions.