High performance numerical methods for moving interface problems and uncertainty analysis

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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.