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

1环境仿真技术在航空航天工业中起着至关重要的作用，并改变了工程设计过程，使该领域更接近于第一时间正确工程的目标。然而，气候变化和其他因素的威胁对更高性能和更高效率的需求意味着需要更准确，鲁棒和强大的仿真工具。能够系统级仿真与多个管理物理laws.2研究aimsThe问题，这个项目寻求答案是：国家的最先进的方法制定，使准确的，强大的，和efficient模拟极端规模multiphysics问题与applicationin航空航天工程？该项目的目标是：发展国家的最先进的，数学上严格的多物理问题的求解器，涉及传热，固体力学，流体力学和电磁学。这里的新奇之处在于数学的解决方法，以更好地捕捉潜在的物理。研究任意高阶精度的方法，使复杂设计的精确仿真成为可能。此外，高阶方法非常适合现代高性能计算体系结构。采用（接近）线性复杂度的算法，以便高效计算极端规模问题的解决方案。这使得系统级仿真成为可能，而不是仅仿真单个/少量组件。研究鲁棒、灵活和高效的耦合技术，适用于航空航天问题中存在的空间和时间尺度之间的巨大差异，这些差异可以相差几个数量级。提出了一种新的基于有限元法的多物理场模拟方案;一个自然的环境，以实现研究目标。这将涉及数学制定新的方法与属性所需的航空航天1应用，以及这些性质的数学证明。所得到的方案将被编程实现，并通过进行各种数值实验和运行基准测试来证明其性能。这些方案将在FeNiCS-X中实现;这是一个强大的、尖端的、开源的有限元库，可以快速、有效地实现最先进的方法。一个关键点是，求解器将在一个统一的框架中实现，允许应用技术，否则是不可能的。此外，本发明还该项目将有助于FeNiCS-X的发展，因为需要的功能还不存在。任何富有成效的方案的性能都将通过解决真实的航空航天问题来证明。该项目产生的所有代码都将免费提供和开放-4相关的EPSRC研究领域有几个EPSRC研究领域，这个项目与以下学科相关：数值分析连续介质力学流体动力学和空气动力学非线性系统数学物理学

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