Efficient approximation and preconditioning strategies for models of swirling flow

Navier-Stokes方程是流体流动数学模型的基本工具。在各种重要的应用领域中，离散形式的方程通常使用计算流体力学软件来求解。这些领域从气象学中的天气预报到航空工程中的节油飞机设计，再到医学物理中的人体心脏模型。该项目的目的是开发新的计算技术，以高效地生成柱面极坐标系中表示的Navier-Stokes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，以确保流动区域中每个点的质量守恒。主要成果将是可证明准确的计算工具和开放源码软件，供其他研究人员进一步使用和开发。这个项目涉及几个国际研究小组正在积极研究的一个主题。研究经费是需要的，以使首席研究人员能够集中和持续地努力解决具有国际竞争力的研究领域中的专题研究问题。

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.