Advanced Finite Element Techniques for Extreme Scale Multiphysics Problems in Aerospace Engineering

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1 ContextSimulation techniques play an essential role in the aerospace industry and have transformed theengineering design process, moving the field closer towards the goal of right-first-time engineering.However, the demand for greater performance and improved effciency driven by the threat ofclimate change and other factors mean that more accurate, robust, and powerful simulation toolsare required; capable of system level simulation with multiple governing physical laws.2 Research aimsThe question this projects seeks to answer is: can state-of-the-art methods be formulated to enableaccurate, robust, and effcient simulations of extreme scale multiphysics problems with applicationsin aerospace engineering? The aims of this project are to: Develop state-of-the-art, mathematically rigorous solvers for multiphysics problems involvingheat transfer, solid mechanics, uid mechanics, and electromagnetism. The novelty here liesin the mathematics of the solution methods to better capture the underlying physics. Investigate methods that are arbitrarily high-order accurate enabling accurate simulation ofintricate designs. In addition, high-order methods are well suited for modern high performancecomputing architecture. Employ algorithms with (near) linear complexity to allow efficient computation of solutionsto extreme scale problems. This enables system level simulation, as opposed to simulatingonly individual/a small number of components.Research robust, exible, and efficient coupling techniques that are suitable for the largedisparities between the spatial and temporal scales present in aerospace problems, which candiffer by several orders of magnitude.3 Novel methodologyThe project will research, develop, and deliver novel multiphysics simulation schemes based on anumerical technique called the finite element method; a natural setting to achieve the research aims.This will involve mathematically formulating new methods with properties desirable for aerospace1applications, as well as mathematical proofs of these properties. The resulting schemes will beimplemented programmatically and their performance demonstrated by conducting various numer-ical experiments and running benchmark tests. The schemes will be implemented in FEniCS-X; apowerful, cutting-edge, open-source finite element library that allows rapid, effcient implementa-tion of state-of-the-art methods. A key point is that the solvers will be implemented in a unifiedframework that allows techniques to be applied that would not otherwise be possible. Additionally,the project will contribute to the development of FEniCS-X as and when features are required thatdo not already exist.The performance of any fruitful schemes will be demonstrated by solving real aerospace problems.All of the resulting code from the project will be made freely available and open-source in the interestof scientific transparency and reproducibility.4 Relevant EPSRC research areasThere are several EPSRC research areas that this project is relevant to, including: Numerical analysis Continuum mechanics Fluid dynamics and aerodynamics Non-linear systems Mathematical physics