Sum-of-Squares Approach to Global Stability and Control of Fluid Flows

Lead Research Organisation: University of Oxford
Department Name: Engineering Science

Abstract

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Description The aim of this project is to understand the properties of systems described by partial differential equations, such as the ones describing the motion of fluids, using computational techniques that do not need to solve these equations.

A major milestone was to be able to computationally verify that certain integral inequalities hold. We have developed a method to do that and this opens the way to apply this method to a number of problems related to dynamical systems in areas such as fluid mechanics, chemical reactions and heat transfer, all described by partial differential equations. This method is being used by other academics to answer questions about their models, without the need to simulate them.
Exploitation Route By using the software package we developed (intsostools, https://github.com/gvalmorbida/INTSOSTOOLS) and also using our mathematical results.
Sectors Environment

URL https://www.imperial.ac.uk/aeronautics/fluiddynamics/sumofsquares/index.php
 
Description The project's aim is to find a way to understand mathematical models of physical systems described by Partial Differential Equations (PDEs) without solving these PDEs. The results we obtained are theoretical and mathematical in nature but we expect that in the future they will be used to result in societal and economical impact. Especially since the final publication of the JFM paper, we expect that industry will be interested in adopting some of our techniques to provide provable bounds on properties of their designs.
First Year Of Impact 2019
Sector Environment
 
Description Collaboration on Sum of Squares and Fluid Mechanics with UCSB 
Organisation University of California, Santa Barbara
Country United States 
Sector Academic/University 
PI Contribution Collaboration, exchange of ideas and knowledge
Collaborator Contribution Collaboration, exchange of ideas and knowledge
Impact Ongoing.
Start Year 2013