Adaptive mesh refinement in fluid-structure interaction in three-dimensions
Lead Research Organisation:
University of Leeds
Department Name: Sch of Computing
Abstract
Recent research at Leeds [1, 2] has developed a novel algorithm for solving fluid-structure interaction (FSI) problems based upon a fictitious domain approach. This has been implemented and tested on model problems in 2-D and 3-D: the former with the use of local mesh refinement on a quadrilateral mesh and the latter based upon a uniform octahedral mesh only.
This project will expand upon the current work in two significant ways: (1) enhancing the efficiency of the 3-D algorithm through the use of (a) mesh adaptivity and (b) preconditioned iterative solvers; (2) applying the method to more practical FSI applications than the model problems so far considered.
1. The 3-D implementation is currently highly time-consuming to run and so we will seek to improve the efficiency in two fundamental ways:
a. By implementing an adaptive mesh approach. This will involve replacing the underlying solver (based upon Taylor-Hood elements on octahedral) by one that is based on equivalent tetrahedral elements and then considering the use of adaptive software on both tetrahedral and hexahedral meshes. Initially the adaptivity will be driven by where the solid-fluid interface is situated but other approaches will then be considered, such as high solution gradients or goal-based error estimation. The use of machine learning to guide the mesh adaptivity may also be considered.
b. By investigating efficient preconditioners for the iterative solution of the linear algebraic equations at each time step. These will be based upon attempts to exploit our knowledge of the structure of the linear systems rather than simply using a "black box" preconditioner (as currently done). It will build upon a substantial body of work that has developed preconditioners for incompressible flows simulated with conforming finite elements.
2. So far only simple model problems have been considered in [1, 2]. We will work with a supervisor from the Institute of Biomedical Engineering (Dr Marlene Mengoni) to apply the techniques developed to a series of challenging 3-D FSI applications arising in the bio-mechanics of joints. These will involve complex 3-d geometries, a variety of solid and material properties and a range of applied forces. As well as providing challenging problems on which to test the methods developed, this collaboration will also support validation of the numerical techniques and an important pathway to potential non-academic impact.
References:
[1] Wang Y; Jimack PK; Walkley MA (2017) A One-Field Monolithic Fictitious Domain Method for Fluid-Structure Interactions. Computer Methods in Applied Mechanics and Engineering, 317, pp. 1146-1168.
[2] Wang Y; Jimack PK; Walkley MA (2019) Energy Analysis for the One-Field Fictitious Domain Method for Fluid-Structure Interactions. Applied Numerical Mathematics, 140, pp. 165-182.
This project will expand upon the current work in two significant ways: (1) enhancing the efficiency of the 3-D algorithm through the use of (a) mesh adaptivity and (b) preconditioned iterative solvers; (2) applying the method to more practical FSI applications than the model problems so far considered.
1. The 3-D implementation is currently highly time-consuming to run and so we will seek to improve the efficiency in two fundamental ways:
a. By implementing an adaptive mesh approach. This will involve replacing the underlying solver (based upon Taylor-Hood elements on octahedral) by one that is based on equivalent tetrahedral elements and then considering the use of adaptive software on both tetrahedral and hexahedral meshes. Initially the adaptivity will be driven by where the solid-fluid interface is situated but other approaches will then be considered, such as high solution gradients or goal-based error estimation. The use of machine learning to guide the mesh adaptivity may also be considered.
b. By investigating efficient preconditioners for the iterative solution of the linear algebraic equations at each time step. These will be based upon attempts to exploit our knowledge of the structure of the linear systems rather than simply using a "black box" preconditioner (as currently done). It will build upon a substantial body of work that has developed preconditioners for incompressible flows simulated with conforming finite elements.
2. So far only simple model problems have been considered in [1, 2]. We will work with a supervisor from the Institute of Biomedical Engineering (Dr Marlene Mengoni) to apply the techniques developed to a series of challenging 3-D FSI applications arising in the bio-mechanics of joints. These will involve complex 3-d geometries, a variety of solid and material properties and a range of applied forces. As well as providing challenging problems on which to test the methods developed, this collaboration will also support validation of the numerical techniques and an important pathway to potential non-academic impact.
References:
[1] Wang Y; Jimack PK; Walkley MA (2017) A One-Field Monolithic Fictitious Domain Method for Fluid-Structure Interactions. Computer Methods in Applied Mechanics and Engineering, 317, pp. 1146-1168.
[2] Wang Y; Jimack PK; Walkley MA (2019) Energy Analysis for the One-Field Fictitious Domain Method for Fluid-Structure Interactions. Applied Numerical Mathematics, 140, pp. 165-182.
Planned Impact
The impact and benefits will reach multiple stakeholders.
(i) CDT Students:- Will develop substantial technical and transferable skills enabling them to build a career and become leaders in industry or academia. In addition to a wide range of computational, modelling and experimental techniques, students will have many opportunities to develop team working, communication and problem solving skills. Students will have very strong career prospects with a wide range of options, including industry and public sector.
(ii) End-user partners:- Will gain access to a pool of at least 50 skilled graduates to innovate in their business and to realise direct impact from research outcomes: new products, processes, and tools. New or strengthened collaborations with academic partners will also follow.
(iii) Academic overseas collaborators:- will share new research outputs, stronger partnerships with Leeds, and knowledge exchange on tools and techniques: thus benefiting research outcomes and researcher training in both countries.
(iv) Other students:- Will have the opportunity to visit Leeds, whilst future students will have access to the new tools and techniques developed by the CDT for learning, thus inspiring new UG/MSc/PhD projects.
(v) Research at Leeds:- We will consolidate our critical mass of fluids-based research through the development of a "cohort of academics", as well as cohorts of students. New research outputs and new collaborations (across Leeds, with industry and overseas) will follow, and we will promote our large body of work coherently with external partners and to the media.
(vi) Other industry:- New tools, processes and techniques developed through research during the CDT will be disseminated via industrial as well as academic routes. We will pro-actively encourage new partners to engage with the CDT as it evolves.
(vii) The economy:- Skilled graduates are key to economic growth and ours will contribute to challenge areas such as energy, the environment, the health sector, as well as those with chronic skills shortage such as the nuclear industry. Innovation, typically in partnership with industry, will lead to economic benefits such as new products, services and spin out.
(viii) Society:- Research leading to new insights into energy, the environment and health challenges will lead to healthier, safer and more efficient environments for the public. Public engagement activities will raise the profile of Fluid Dynamics, and enable the public to understand its enormous breadth of application, and importance, to real world problems.
Evidence for impact creation comes partly from government sponsored reports pointing to the need for well-trained graduates in fluid dynamics, and also from the many letters of support we have received from our partners. In consumer products P&G tell us that "within our current product portfolio, fluids feature in 21 of our 24 one billion dollar brands (more than $1 billion sales) which include detergents, shampoos, fabric softener, dishwashing liquid, batteries, toothpaste and cosmetics". In engineering design Parker Hannifin believe that "the UK will need a greater number of graduates with complementary skills in high fidelity CFD and optimisation methods". There is a similar demand in the environmental sector. For example the National Oceanography Centre state that "in the coming years we expect to build our technical expertise in areas such as numerical methods, unstructured gridding and solvers, ocean dynamics, buoyancy driven flows and ensemble methods for uncertainty estimates", while HR Wallingford "expect to require access to expertise in relevant physical processes, compressible/incompressible flow, physical model scaling, numerical methods, multi-phase flow, atmospheric flows".
(i) CDT Students:- Will develop substantial technical and transferable skills enabling them to build a career and become leaders in industry or academia. In addition to a wide range of computational, modelling and experimental techniques, students will have many opportunities to develop team working, communication and problem solving skills. Students will have very strong career prospects with a wide range of options, including industry and public sector.
(ii) End-user partners:- Will gain access to a pool of at least 50 skilled graduates to innovate in their business and to realise direct impact from research outcomes: new products, processes, and tools. New or strengthened collaborations with academic partners will also follow.
(iii) Academic overseas collaborators:- will share new research outputs, stronger partnerships with Leeds, and knowledge exchange on tools and techniques: thus benefiting research outcomes and researcher training in both countries.
(iv) Other students:- Will have the opportunity to visit Leeds, whilst future students will have access to the new tools and techniques developed by the CDT for learning, thus inspiring new UG/MSc/PhD projects.
(v) Research at Leeds:- We will consolidate our critical mass of fluids-based research through the development of a "cohort of academics", as well as cohorts of students. New research outputs and new collaborations (across Leeds, with industry and overseas) will follow, and we will promote our large body of work coherently with external partners and to the media.
(vi) Other industry:- New tools, processes and techniques developed through research during the CDT will be disseminated via industrial as well as academic routes. We will pro-actively encourage new partners to engage with the CDT as it evolves.
(vii) The economy:- Skilled graduates are key to economic growth and ours will contribute to challenge areas such as energy, the environment, the health sector, as well as those with chronic skills shortage such as the nuclear industry. Innovation, typically in partnership with industry, will lead to economic benefits such as new products, services and spin out.
(viii) Society:- Research leading to new insights into energy, the environment and health challenges will lead to healthier, safer and more efficient environments for the public. Public engagement activities will raise the profile of Fluid Dynamics, and enable the public to understand its enormous breadth of application, and importance, to real world problems.
Evidence for impact creation comes partly from government sponsored reports pointing to the need for well-trained graduates in fluid dynamics, and also from the many letters of support we have received from our partners. In consumer products P&G tell us that "within our current product portfolio, fluids feature in 21 of our 24 one billion dollar brands (more than $1 billion sales) which include detergents, shampoos, fabric softener, dishwashing liquid, batteries, toothpaste and cosmetics". In engineering design Parker Hannifin believe that "the UK will need a greater number of graduates with complementary skills in high fidelity CFD and optimisation methods". There is a similar demand in the environmental sector. For example the National Oceanography Centre state that "in the coming years we expect to build our technical expertise in areas such as numerical methods, unstructured gridding and solvers, ocean dynamics, buoyancy driven flows and ensemble methods for uncertainty estimates", while HR Wallingford "expect to require access to expertise in relevant physical processes, compressible/incompressible flow, physical model scaling, numerical methods, multi-phase flow, atmospheric flows".
Organisations
People |
ORCID iD |
Peter Jimack (Primary Supervisor) | |
Gregory Walton (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
NE/W503125/1 | 31/03/2021 | 30/03/2022 | |||
2105464 | Studentship | NE/W503125/1 | 30/09/2018 | 28/02/2023 | Gregory Walton |