Towards surrogate models of large scale parametric industrial flow problems

大规模参数化工业流程问题的替代模型

• 批准号: 2610494
• 金额: --
• 依托单位: Loughborough University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2610494
• 关键词: Towards; surrogate; models; large; scale

Computer simulations are an increasingly important tool to support virtual prototyping in science and engineering as they enable to reduce the time and cost of experimental testing. Virtual design aims to identify the best configuration of a system by testing several values of parameters that characterise various aspects such as geometric features (e.g., the length of a beam) or material properties (e.g., the density of a fluid). These quantities are incorporated in the mathematical model of the system by parametrising the underlying equations. The resulting parametric problem is then solved numerically to identify the optimal configurations. However, this task is computationally very demanding. In fact, in practical 3D applications, numerical models can involve millions of unknowns and must be solved multiple times for each possible configuration of the system. Novel fast and reliable algorithms are thus needed to make the computational cost affordable. This is a very challenging research area of great practical importance for many applications such as optimal design of filtration systems and aerodynamic simulations in the automotive industry. This project will contribute to this field by developing a new computational framework that combines two mathematical methods: domain decomposition and proper generalised decomposition. These will be used to split parametric problems into collections of simpler subproblems, to solve them independently accounting for all significant values of the parameters, and to 'glue' the local solutions to obtain those of the original problems. The proposed project will contribute to advance the state-of-the-art in numerical mathematics and develop effective algorithms for scientists and engineers that use virtual design by computational modelling.

计算机仿真是一个越来越重要的工具，以支持虚拟样机在科学和工程，因为他们能够减少实验测试的时间和成本。虚拟设计的目的是通过测试几个参数值来确定系统的最佳配置，这些参数值包括各个方面，例如几何特征（例如，梁的长度）或材料特性（例如，流体的密度）。这些量通过对基本方程进行参数化而并入系统的数学模型中。由此产生的参数问题，然后解决数值识别的最佳配置。然而，这个任务在计算上是非常苛刻的。事实上，在实际的3D应用中，数值模型可能涉及数百万个未知数，并且必须针对系统的每个可能配置多次求解。因此，需要新的快速和可靠的算法，使计算成本负担得起的。这是一个非常具有挑战性的研究领域，对于许多应用具有重要的实际意义，例如过滤系统的优化设计和汽车工业中的空气动力学模拟。该项目将通过开发一个新的计算框架来促进这一领域的发展，该框架结合了两种数学方法：区域分解和适当的广义分解。这些将被用来分裂成更简单的子问题的集合参数的问题，解决他们独立占所有重要的参数值，并“胶水”的本地解决方案，以获得那些原始问题。拟议的项目将有助于推进最先进的数值数学，并为科学家和工程师开发有效的算法，通过计算建模进行虚拟设计。