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

仿真技术在航空航天工业中发挥着至关重要的作用，并改变了工程设计过程，使该领域更接近于正确的首次工程目标。然而，由于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、更健壮和更强大的模拟工具；具有多种控制物理定律的系统级仿真能力研究目的本项目试图回答的问题是：是否可以制定最先进的方法来实现精确，稳健和有效的模拟极端尺度多物理场问题与航空航天工程的应用？该项目的目标是：为涉及传热、固体力学、流体力学和电磁学的多物理场问题开发最先进的、数学上严格的求解器。这里的新颖之处在于解决方法的数学，以更好地捕捉潜在的物理。研究任意高阶精确的方法，使复杂设计的精确模拟成为可能。此外，高阶方法非常适合现代高性能计算体系结构。采用具有（接近）线性复杂性的算法，以便有效地计算极端规模问题的解决方案。这使系统级模拟成为可能，而不是只模拟单个/少量组件。研究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的稳健、灵活和有效的耦合技术，这些差异可能存在几个数量级的差异新方法：该项目将研究、开发和提供基于称为有限元法的数值技术的新型多物理场模拟方案；实现研究目标的自然环境。这将涉及在数学上制定具有航空航天应用所需特性的新方法，以及这些特性的数学证明。所得到的方案将以编程方式实现，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中实施；强大的，前沿的，开源的有限元库，允许快速，有效地实现最先进的方法。关键的一点是，求解器将在一个统一的框架中实现，允许应用否则不可能应用的技术。此外，该项目将有助于FEniCS-X的开发，当需要的功能还不存在时。任何富有成效的方案的性能都将通过解决实际的航空航天问题来证明。出于科学透明度和可重复性的考虑，项目产生的所有代码都将免费提供和开放源代码EPSRC的相关研究领域本项目涉及EPSRC的几个研究领域，包括：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

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