Modelling hyperbolic and elliptic elasticity with discontinuous coefficients using an error driven adaptive isogeometric basis

使用误差驱动的自适应等几何基础对具有不连续系数的双曲和椭圆弹性进行建模

• 批准号: EP/W023202/1
• 负责人: Adriana Paluszny Rodriguez
• 金额: $ 9.75万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW023202%2F1
• 关键词: Modelling; hyperbolic; elliptic; elasticity; discontinuous

The UK has pledged to achieve net zero emissions by 2050, aiming to develop green transition technologies such as geothermal energy, geological storage of CO2 from industrial and direct air capture sources, hydrogen fuel cells, batteries, and compressed-air energy, as well as advancing nuclear as a clean energy source through clean storage and disposal. The success of these technologies is highly dependent on understanding the behaviour of Earth materials at a range of scales, in the context of deformation, fluid flow, and temperature changes, which can affect how rocks break and how fluids and heat migrate in the subsurface through these rocks. Understanding how fractures and other smaller-scale heterogeneities affect rock properties also furthers the capabilities of numerical models dedicated to predicting fractures in ceramics, composites, bioengineered materials, human bones, and ion lithium batteries, as additional examples.Processes governing fracturing in complex media, and the interaction of fractures with smaller and larger scale discontinuities and material variations, is often investigated using numerical models. The main drawback of these models is that their performance usually depends on the amount of detail included, such as the geometric details of the ensuing fractures, and distributions of differently shaped embedded inclusions that tend to change the material's behaviour. However, having the ability to effectively and accurately model real full-scale heterogeneous multi-scale problems is necessary to the development of robust, low-carbon and cost-effective strategies that underpin the energy transition. This project proposes to develop a key mathematical strategy to enhance the performance of computational solid mechanics methods, while incorporating additional levels of detail in the description of the material. We propose to develop, implement, and validate an efficient three-dimensional multi-scale numerical method, that combines 3D volumetric isogeometry in bodies containing fractures, with numerical error estimators to more efficiently represent mm- and cm-scale heterogeneities when computing the deformation of a meter- to km-scale body containing multiple fractures. Error estimators enable regions critical to overall solution accuracy to be targeted with higher levels of computational power, dynamically adjusting detail and load during the simulation. As opposed to other methods, the specific method to be developed during this project supports both small and large variations in the material properties, without compromising the quality of the solution, and without inflating the computational cost of the method. Computational efficiency and accuracy enable the method to be applied effectively to large real-world problems, enabling the consideration of larger and more realistic problems without significantly increasing computational effort. Developing the ability to model such problems, and sharing the development through open-source code with the wider scientific community, is of national importance. Quantifying the relationship between scales in the context of solid body fracturing, in complex scenarios, directly supports responsible innovation in the UK, and supports the development of low-carbon and effective energy generation schemes, safe and clean deposition of waste materials, and elongating the life and increasing the efficacy of electrical storage devices.

英国承诺到2050年实现净零排放，目标是开发地热能、工业和直接空气捕获源二氧化碳地质储存、氢燃料电池、电池和压缩空气等绿色转型技术。空气能源，以及通过清洁储存和处置推动核能成为清洁能源。这些技术的成功在很大程度上取决于在变形、流体流动和温度变化的背景下，在一系列尺度上理解地球材料的行为，这些行为会影响岩石如何破裂以及流体和热量如何通过这些岩石在地下迁移。了解裂缝和其他较小尺度的非均匀性如何影响岩石性质，也进一步提高了数值模型的能力，这些数值模型致力于预测陶瓷、复合材料、生物工程材料、人类骨骼和离子锂电池中的裂缝，作为额外的例子。复杂介质中控制裂缝的过程，以及裂缝与较小和较大尺度的不连续性和材料变化的相互作用，通常使用数值模型进行研究。这些模型的主要缺点是，它们的性能通常取决于所包含的细节量，例如随后断裂的几何细节，以及倾向于改变材料行为的不同形状的嵌入式夹杂物的分布。然而，有能力有效和准确地模拟真实的全尺度异构多尺度问题是必要的，以发展强大的，低碳和具有成本效益的战略，支持能源转型。该项目提出开发一种关键的数学策略，以提高计算固体力学方法的性能，同时在材料描述中加入额外的细节。我们建议开发，实施，并验证一个有效的三维多尺度数值方法，该方法结合了三维体积等几何包含骨折的机构，数值误差估计更有效地代表毫米和厘米级的异质性时，计算变形的米到公里级的身体包含多个裂缝。误差估计器使对整体解决方案准确性至关重要的区域能够以更高级别的计算能力为目标，在仿真期间动态调整细节和负载。与其他方法相反，在该项目期间开发的特定方法支持材料特性的小变化和大变化，而不会影响解决方案的质量，也不会增加该方法的计算成本。计算效率和准确性使该方法能够有效地应用于大型现实问题，从而能够在不显著增加计算工作量的情况下考虑更大和更现实的问题。发展模拟这些问题的能力，并通过开放源代码与更广泛的科学界分享发展成果，对国家具有重要意义。在复杂的情况下，在固体压裂的背景下量化规模之间的关系，直接支持英国负责任的创新，并支持低碳和有效的能源生产计划的发展，安全和清洁的废料沉积，延长寿命和提高电力存储设备的功效。