Efficient approximation and preconditioning strategies for models of swirling flow

旋流流模型的高效逼近和预处理策略

• 批准号: EP/W033801/1
• 负责人: David Silvester
• 金额: $ 6.99万
• 依托单位: University of Manchester
• 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: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW033801%2F1
• 关键词: Efficient; approximation; preconditioning; strategies; models

The Navier-Stokes equations are a fundamental tool for the mathematical modelling of fluid flow. Discretised versions of the equations are routinely solved using computational fluid dynamics software in a variety of important application areas. These range from weather prediction in meteorology to the design of fuel-efficient aeroplanes in aeronautical engineering to human heart modelling in medical physics.The aim of this project is to develop new computational techniques for efficiently generating numerical solutions of the Navier-Stokes equations expressed in a cylindrical polar coordinate system. In particular, we will design, analyse and test novel approximation strategies that ensure mass conservation at every point in the flow region. The main deliverables will be provably accurate computational tools and open-source software for other researchers to use and develop further.This project addresses a topic that several international research groups are actively working on. Research funding is needed to enable the principal investigator to make a focused and sustained effort in attacking a topical research problem in an internationally competitive research area.

Navier-Stokes方程是流体流动数学建模的基本工具。在各种重要的应用领域中，使用计算流体动力学软件对方程的离散化版本进行常规求解。这一项目的范围从气象学的天气预报到航空工程中的节能飞机的设计，再到医学物理学中的人体心脏模型，其目的是发展新的计算技术，以便有效地产生以圆柱极坐标系表示的纳维尔-斯托克斯方程的数值解。特别是，我们将设计，分析和测试新的近似策略，以确保在流动区域的每一点的质量守恒。主要成果将是可证明准确的计算工具和开放源代码软件，供其他研究人员使用和进一步开发。本项目涉及一个多个国际研究小组正在积极研究的课题，需要研究资金，使首席研究员能够集中精力和持续努力，在国际竞争激烈的研究领域解决一个热门的研究问题。

项目成果

IFISS3D: A Computational Laboratory for Investigating Finite Element Approximation in Three Dimensions

IFISS3D：研究三维有限元近似的计算实验室

• DOI: 10.1145/3604934
• 发表时间: 2023
• 期刊: ACM Transactions on Mathematical Software
• 影响因子: 2.7
• 作者: Papanikos G