Prof Matthias Heil

Professor of Applied Mathematics at the School of Mathematics at the University of Manchester.



[People] [Research] [Publications] [Teaching] [Admin] [Seminars] [Editorial responsbilities/Refereeing] [Family] [Animations] [Contact]


People

Here are some people I work with: ...and here are some former PhD students/postdocs:

Research Interests: Computational Mechanics and Biomechanics.

[Check out this recent article in the EPSRC Newsline magazine.]

Scientific Computing:
oomph-lib -- the object-oriented multi-physics finite-element library

Fluid-structure interaction problems

(Flow in collapsible tubes).

Airway reopening:

The propagation of an air finger into a collapsed elastic tube.

Airway closure:
Static liquid bridges in elastic tubes.

Airway closure:
Surface-tension-driven instabilities in elastic tubes.

Computational fluid dynamics.

Finite element methods.

Large displacement shell theory.

Experimental methods.


Publications

Crane, L.J. & Heil, M. (1995) The Summation of Slowly Convergent Double Series and Application to Fluid-Mechanics. Zeitschrift fur angewandte Mathematik und Mechanik 75 , 403-407. (abstract)

Heil, M. & Pedley, T.J. (1995) Large Axisymmetric Deformations of a Cylindrical Shell Conveying a Viscous Flow. Journal of Fluids and Structures 9, 237-256. (abstract)

Heil, M. (1996) The Stability of Cylindrical Shells Conveying Viscous Flow. Journal of Fluids and Structures 10, 173-196. (abstract) (pdf) (ps)

Heil, M. & Pedley, T.J. (1996) Large Post-Buckling Deformations of Cylindrical Shells Conveying Viscous Flow. Journal of Fluids and Structures 10 , 565-599. (abstract) (pdf) (ps)

Heil, M. (1997), Stokes Flow in Collapsible Tubes -- Computation and Experiment. Journal of Fluid Mechanics 353, 285-312. (abstract)(ps preprint)

Heil, M. (1998) Stokes Flow in an Elastic Tube -- A Large-Displacement Fluid-Structure Interaction Problem. The International Journal for Numerical Methods in Fluids 28, 243-265. (abstract)(pdf preprint)

Heil, M. (1999) Minimal Liquid Bridges in Non-Axisymmetrically Buckled Elastic Tubes. Journal of Fluid Mechanics 380, 309-337. (abstract) (ps preprint)

Heil, M. (1999) Airway Closure: Liquid Bridges in Strongly Buckled Elastic Tubes. ASME Journal of Biomechanical Engineering 121, 487-493. (ps preprint) (abstract)

Heil, M. (2000) Finite Reynolds number effects in the propagation of an air finger into a liquid-filled flexible-walled channel. Journal of Fluid Mechanics 424, 21-44.(ps preprint) (abstract)

Heil, M. (2001) The Bretherton problem in elastic-walled channels: Finite Reynolds number effects. In: IUTAM Symposium on Free Surface Flows, Editors: A. C. King & Y.D. Shikmurzaev. Kluwer, Dordrecht, Netherlands. pp. 113-120. (ps preprint) (abstract)

Heil, M. (2001) Finite Reynolds number effects in the Bretherton problem. Physics of Fluids 13, 2517-2521. (ps preprint) (abstract)

Heil, M. & Hazel, A. L. (2001) PROSPER: LATEX -based computer presentations. SIAM News 34(10), 19-20. (pdf reprint). (html version of this article with all files).

Heil, M. & White, J.P. (2002) Airway Closure: Surface-tension-driven non-axisymmetric instabilities of liquid-lined elastic rings. Journal of Fluid Mechanics 462, 79-109. (ps preprint)(abstract)

Hazel, A. L. & Heil, M. (2002) The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section. Journal of Fluid Mechanics 470, 91-114. (pdf preprint) (abstract)

Heil, M. & Jensen, O.E. (2003) Flows in deformable tubes and channels -- Theoretical models and biological applications. Chapter 2 of: Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries. Eds: T.J. Pedley and P.W. Carpenter. pp. 15-50. Kluwer, Dordrecht, Netherlands. (pdf preprint)(abstract)

Hazel, A. L. & Heil, M. (2003) Three-dimensional airway reopening: The steady propagation of a semi-infinite bubble into a buckled elastic tube. Journal of Fluid Mechanics 478 47-70. (pdf preprint) (abstract)

Jensen, O.E. & Heil, M. (2003) High-frequency self-excited oscillations in a collapsible-channel flow. Journal of Fluid Mechanics 481 235-268. (pdf preprint) (abstract)

Hazel, A. L. & Heil, M. (2003) Steady finite-Reynolds-number flows in three-dimensional collapsible tubes. Journal of Fluid Mechanics 486 79-103. (pdf preprint)(abstract)

Heil, M. & Hazel, A. L. (2003) Mass transfer from a finite strip near an oscillating stagnation point --- implications for atherogenesis. Journal of Engineering Mathematics. 47 315-334. (abstract)(pdf preprint)

Heil, M. (2004) An efficient solver for the fully-coupled solution of large-displacement fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering. 193 1-23. (abstract) (pdf preprint)

Watton, P. N., Hill, N. A. & Heil, M. (2004) A mathematical model for the growth of the abdominal aortic aneurysm. Biomechanics and Modeling in Mechanobiology 3 98-113. (abstract) (pdf reprint)

White, J.P. & Heil, M. (2005) Three-dimensional instabilities of liquid-lined elastic tubes -- a lubrication theory model. Physics of Fluids 17 (abstract) (pdf preprint)

Hazel, A. L. & Heil, M. (2005) Surface-tension-induced buckling of liquid-lined elastic tubes -- a model for pulmonary airway closure. Proceedings of the Royal Society A 461, 1847-1868.(abstract) (pdf preprint)

Heil, M. & Waters, S.L. (2006) Transverse flows in rapidly oscillating, elastic cylindrical shells. Journal of Fluid Mechanics 547, 185-214. (abstract) (pdf preprint)

Baroud, C.N., Tsikata, S. & Heil, M. (2006) The propagation of low-viscosity fingers into fluid-filled, branching networks. Journal of Fluid Mechanics 546, 285-294. (abstract) (pdf preprint)

Hazel, A. L. & Heil, M. (2006) Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening. ASME Journal of Biomechanical Engineering 128, 573-578. (abstract) (pdf preprint)

Heil, M. & Hazel, A. L. (2006) oomph-lib -- An Object-Oriented Multi-Physics Finite-Element Library. In: Fluid-Structure Interaction, Editors: M. Schafer und H.-J. Bungartz. Springer (Lecture Notes on Computational Science and Engineering), pp. 19--49. (abstract) (pdf preprint)

Heil, M. & Waters, S.L. (2008) How rapidly oscillating collapsible tubes extract energy from a viscous mean flow. Journal of Fluid Mechanics 601, 199-227. (abstract) (pdf preprint)

Hazel, A.L. & Heil, M. (2008) The influence of gravity on the steady propagation of a semi-infinite bubble into a flexible channel. Physics of Fluids 20, 092109. (abstract) (pdf preprint)

Heil, M., Hazel, A.L. & Boyle, J. (2008) Solvers for large-displacement fluid-structure interaction problems: Segregated vs. monolithic approaches. Computational Mechanics 43, 91-101. (abstract) (pdf preprint)

Heil, M., Hazel, A.L. & Smith, J.A. (2008) The Mechanics of Airway Closure Respiratory Physiology & Neurobiology 163, 214-221. (abstract) (pdf preprint)

Muddle, R.L., Boyle, J.W., Mihajlovic, M.D. & Heil, M. (2009) : The Development of an Object-Oriented Parallel Block Preconditioning Framework Parallel scientific computing and optimization: Advances and applications 27, 37-46 (abstract)

Whittaker, R.J., Waters, S.L., Jensen, O.E., Boyle, J. & Heil, M. (2010) The energetics of flow through a rapidly oscillating tube. Part I: General theory. Journal of Fluid Mechanics 648, 83-121 (abstract) (pdf)

Whittaker, R.J., Heil, M., Boyle, J., Jensen, O.E., & Waters, S.L. (2010) The energetics of flow through a rapidly oscillating tube. Part II: Application to an elliptical tube. Journal of Fluid Mechanics 648, 123-153 (abstract) (pdf)

Heil, M., Boyle, J. (2010) Self-excited oscillations in three-dimensional collapsible tubes: Simulating their onset and large-amplitude oscillations. Journal of Fluid Mechanics 652, 405-426 (abstract) (pdf)

Whittaker, R.J., Heil, M., Jensen, O.E., & Waters, S.L. (2010) A rational derivation of a tube law from shell theory. Quarterly Journal of Mechanics and Applied Mathematics (pdf) (abstract)

Whittaker, R.J., Heil, M., Jensen, O.E., & Waters, S.L. (2010) The onset of high-frequency self-excited oscillations in elastic-walled tubes. Proceedings of the Royal Society A 466, 3635-3657. (abstract) (pdf)

Stewart, P.S., Heil, M., Waters, S.L. & Jensen, O.E. (2010) Sloshing and slamming oscillations in collapsible channel flow. Journal of Fluid Mechanics 662, 288-319. (abstract) (pdf) (Supplementary material (movie))

Heil, M., Hazel, A. L. (2011) Fluid-structure interaction in internal physiological flows. Annual Review of Fluid Mechanics 43, 141-162. (abstract). (pdf)

Whittaker, R.J., Heil, M., & Waters, S.L. (2011) The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. Philosophical Transactions of the Royal Society A 369, 2989-3006. (abstract) (pdf)

Hazel, A. L., Heil, M., Waters, S.L. & Oliver, J.M. (2012) On the liquid lining in fluid-conveying curved tubes. Journal of Fluid Mechanics 705, 213-233. DOI: 10.1017/jfm.2011.346

Pihler-Puzovic, D., Illien, P., Heil, M. & Juel, A. (2012) Suppression of Complex Fingerlike Patterns at the Interface between Air and a Viscous Fluid by Elastic Membranes. Phys. Rev. Lett. 108. DOI: 10.1103/PhysRevLett.108.074502

Heil, M., Kharrat, T., Cotterill, P.A. & Abrahams, I.D. (2012) Quasi-resonances in sound-insulating coatings. Journal of Sound and Vibration 331 4774-4784. DOI: 10.1016/j.sv.2012.05.029

Muddle, R.L., Mihajlovic, M. & Heil, M. (2012) An efficient preconditioner for monolithically-coupled large-displacement fluid-structure interaction problems with pseudo-solid mesh updates. Journal of Computational Physics 231, 7315-7334. DOI: 10.1016/j.jcp.2012.07.001

Pihler-Puzovic, D., Perillat, R., Russell, M., Juel, A. & Heil, M. (2013) Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells. Journal of Fluid Mechanics 731, 162-183 DOI: 10.1017/jfm.2013.375

Pihler-Puzovic, D., Juel, A. & Heil, M. (2014) The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells. Physics of Fluids 26, 022102. DOI: doi:10.1063/1.4864188.

Shepherd, D., Miles, J., Heil, M., Mihajlovic, M. (2014) Discretisation induced stiffness in micromagnetic simulations. IEEE Trans. Magn., 50(11) 7201304. DOI: 10.1109/TMAG.2014.2325494

Evatt, G.W., Abrahams, I.D., Heil, M., Mayer, C., Kingslake, J., Mitchell, S.L., Fowler, A.C. & Clark, C.D. (2015) Glacial melt under a debris layer: the DADDI model. Journal of Glaciology 61, 825-836. DOI: 10.3189/2015JoG14J235. (pdf)

Cimpeanu, R., Martinsson, A. & Heil, M. (2015) A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation. Journal of Computational Physics 296 329347. DOI: doi:10.1016/j.jcp.2015.05.006.

Heil, M. & Hazel, A.L. (2015) Flow in flexible/collapsible tubes. In: Fluid-Structure Interactions in Low-Reynolds-Number Flows. Eds: Duprat, C. & Stone, H.A. Royal Society of Chemistry, RSC Publishing. pp. 280-311. See details on the publisher's webpage.

Pihler-Puzovic, D., Juel, A., Peng, G., Lister, J. & Heil, M. (2015) Displacement flows under elastic membranes. Part 1: Experiments and direct numerical simulations. Journal of Fluid Mechanics 784 487- 511. DOI: doi:10.1017/jfm.2015.590. (pdf)

Peng, G., Pihler-Puzovic, D., Juel, A., Heil, M. & Lister, J. (2015) Displacement flows under elastic membranes. Part 2: Analysis of interfacial effects. Journal of Fluid Mechanics 784 512- 547. DOI: doi:10.1017/jfm.2015.589. (pdf)

Pestana, J., Muddle, R., Heil, M., Tisseur, F. & Mihajlovic M. (2015) Efficient block preconditioning for a C1 finite element discretisation of the Dirichlet biharmonic problem. SIAM Journal on Scientific Computing (in print)


Teaching

Current courses

Previous courses

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Admin

Currently, my main administrative job is to act as the School's Postgraduate Director (Admissions). In the past I used to be responsible for the following administrative jobs:

Applied & NA Seminars

I used to be in charge of organising the Applied & NA Seminars in our department. Now Rich Hewitt has taken over.

Reviewing/Editorial responsibilities

I am an Associate Editor for the

I am a member of the EPSRC College and regularly act as a referee for the following journals


.

Meet the family!

[very old pictures]

Some interesting fluids animations:

I have copied these movies from the ITSC Fluids Movie Archive so they download faster.


How to contact me:

Email: M.Heil@maths.manchester.ac.uk
Snail Mail: School of Mathematics
University of Manchester
Oxford Road
Manchester M13 9PL
U.K.

Phone: +44 (0)161 275 5808
Fax: +44 (0)161 275 5819
WWW: http://www.maths.man.ac.uk/~mheil/ (this page)


Page last modified: January 8, 2008


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