Efficient approximation and preconditioning strategies for models of swirling flow

Lead Research Organisation: The University of Manchester
Department Name: Mathematics

Abstract

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.
 
Description Pestana-Silvester collaboration 
Organisation University of Strathclyde
Department Mathematics and Statistics Strathclyde
Country United Kingdom 
Sector Academic/University 
PI Contribution We have coauthored one research output to date. We are working on a follow-up publication.
Collaborator Contribution We have coauthored one research output to date. We are working on a follow-up publication.
Impact Pestana, J. and Silvester D. Fast solution of incompressible flow problems with two-level pressure approximation, arXiv.2303.10233 {https://doi.org/10.48550/arXiv.2303.10233}
Start Year 2022
 
Title IFISS3D 
Description IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three space dimensions. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error estimation, as well as iterative solvers. The package is designed to be useful as a teaching tool for instructors and students who want to learn about state-of-the-art finite element methodology. It will also be useful for researchers as a source of reproducible test matrices of arbitrarily large dimension. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
Impact The package is designed to be useful as a teaching tool for instructors and students who want to learn about state-of-the-art finite element methodology. It will also be useful for researchers as a source of reproducible test matrices of arbitrarily large dimension.