Sarah Mitchell's home page


Sarah Mitchell (MMath, Ph.D)

Position:
Lecturer in Applied Mathematics
Address:
Department of Mathematics & Statistics
University of Limerick
Limerick
Ireland
Telephone Number:
+353-61-202259
Fax:
+353-61-334927
Email:
sarah.mitchell@ul.ie

Seminars

I organise the MACSI seminars in the department of Mathematics and Statistics at UL. Here is a list of the Autumn Semester 2014 schedule.

Teaching: (Autumn Semester 2014/15)

Here is my teaching page for MS4021 (Calculus 1) and MA4001 (Engineering Mathematics 1).

Research Interests

My research interests are mainly focussed on the numerical and mathematical modelling of moving boundary problems relevant to solidification, melting and polymer diffusion. The numerical aspects of this work are joint with Dr. Michael Vynnycky from UL and the modelling aspects with Prof. Tim Myers from Centre de Recerca Matematica, Barcelona and Prof. Stephen O'Brien from UL.

I also work on numerical and mathematical modelling of hydraulic fractures (or fluid-driven) fractures in rocks. This is joint work with Prof. Anthony Peirce and Prof. Rachel Kuske from the University of British Columbia, Vancouver.

I am also part of Stokes Professor Andrew Fowler's biofilm group working on mathematical models of bioremediation of polluted groundwater flow. We are currently co-supervising Ph.D student Laura Cribbin.

One day I'd like to get back to research into numerical solution of conservation laws with application to chemical pollutants in groundwater flow which continues my Ph.D project with supervisors Prof. Alastair Spence and Prof. Bill Morton.

Here is my google scholar page.

An up-to-date copy of my CV can be found here and below is a list of my publications:

  • M. Vynnycky, S. L. Mitchell, "On the Accuracy of a Finite-Difference Method for Parabolic PDEs with Discontinuous Boundary Conditions", Numerical Heat Transfer, Part B, in press.
  • M. Vynnycky, W. T. Lee, S. L. Mitchell, G. Richardson, "Foam formation in the plastics industry", Mathematics-in-Industry Cast Studies Journal, 5, 27-42, 2013.
  • F. Font, S. L. Mitchell, T. G. Myers. "One-dimensional solidification of supercooled melts", International Journal of Heat and Mass Transfer, 62, 411-421, 2013.
  • T. G. Myers, S. L. Mitchell, "A mathematical analysis of the motion of an in-flight soccer ball", Sports Engineering, 16, 29-41, 2013.
  • S. L. Mitchell, S. O. B. O'Brien, "Asymptotic, numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers", Applied Mathematics and Computation, 219, 376-388, 2012.
  • S. L. Mitchell, T. G. Myers, "Application of heat balance integral methods to one-dimensional phase change problems", International Journal of Differential Equations, Vol. 2012, 187902, 22 pages.
  • T. G. Myers, S. L. Mitchell, F. Font, "Energy conservation in the one-phase supercooled Stefan problem", International Communications in Heat and Mass Transfer, International Communications in Heat and Mass Transfer, 39, 1522-1525, 2012.
  • S. L. Mitchell, M. Vynnycky, "An accurate finite-difference method for ablation-type Stefan problems", Journal of Applied and Computational Mathematics, 236, 4181-4192, 2012.
  • S. L. Mitchell, "Applying the combined integral method to one-dimensional ablation", Applied Mathematical Modelling, 36, 127-138, 2012.
  • S. L. Mitchell, "An accurate nodal heat balance method with spatial subdivision", Numerical Heat Transfer, Part B, 60, 34-56, 2011.
  • T. G. Myers, S. L. Mitchell, "Application of the Combined Integral Method to Stefan problems", Applied Mathematical Modelling, 35, 4281-4294, 2011.
  • S. L. Mitchell, M. Vynnycky, I. G. Gusev, S. S. Sazhin, "An accurate numerical solution for the transient heating of an evaporating spherical droplet", Applied Mathematics and Computation, 217, 9219-9233, 2011.
  • S. L. Mitchell, T. G. Myers, "Improving the accuracy of heat balance methods applied to thermal problems with time dependent boundary conditions", International Journal of Heat and Mass Transfer, 53, 3540-3551, 2010.
  • S. L. Mitchell, T. G. Myers, "Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems", SIAM Review, 52(1), 57-86, 2010.
  • M. Vynnycky, S. L. Mitchell, "Evaporative cooling and the Mpemba effect", Heat and Mass Transfer, 46, 881-890, 2010.
  • T. G. Myers, S. L. Mitchell, "Mathematical Modelling of Phase Change with a Flowing Thin Film", Progress in Industrial Mathematics at ECMI 2010, 399-405.
  • S. L. Mitchell, "Approximate solution methods for the one-dimensional Stefan problem with Kinetic Undercooling", 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, July 2010.
  • M. Vynnycky, S. L. Mitchell, "On the solution of Stefan problems with delayed onset of phase-change", 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, July 2010.
  • S. L. Mitchell, M. Vynnycky, "Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems", Applied Mathematics and Computation, 215, 1609-1621, 2009.
  • T. G. Myers, S. L. Mitchell, "Application of the heat balance and refined heat balance integral methods to the Korteweg-de Vries equation", Thermal Science, 13(2), 112-119, 2009.
  • T. G. Myers, S. L. Mitchell, G. Muchatibaya, "Unsteady contact melting of a rectangular cross-section phase change material", Physics of Fluids, 20 (103101), 2008.
  • S. L. Mitchell, T. G. Myers, "Heat Balance Integral Method for One-Dimensional Finite Ablation", AIAA Journal of Thermophysics and Heat Transfer, 22(3), 508-514, 2008.
  • S. L. Mitchell, T. G. Myers, "Approximate solution methods for one-dimensional solidification from an incoming fluid", Applied Mathematics and Computation, 202(1), 311-326, 2008.
  • T. G. Myers, S. L. Mitchell, G. Muchatibaya, M. Y. Myers, "A cubic heat balance integral method for one-dimensional melting of a finite thickness layer", International Journal of Heat and Mass Transfer, 50, 5307-5315, 2007.
  • S. L. Mitchell, R. Kuske, A. P. Peirce, "An asymptotic framework for the analysis of hydraulic fractures: the impermeable case", Journal of Applied Mechanics, 74, 365-372, 2007.
  • S. L. Mitchell, R. Kuske, A. P. Peirce, "An asymptotic framework for finite hydraulic fractures including leak-off", SIAM Journal on Applied Mathematics, 67(2), 364-386, 2007.
  • S. L. Mitchell, T. G. Myers, "The laminar-turbulent transition of yield stress fluids in large pipes", Proceedings of the 3rd Mathematics in Industry Study Group, University of Witwatersrand, January 2007.
  • S. L. Mitchell, K. W. Morton, A. Spence, "Analysis of box schemes for reactive flow problems", SIAM Journal on Scientific Computing, 27(4), 1202-1225, 2006.
  • Other Interests

    Ceramics: here are some pictures of my recent work and older work.

    Rugby: Go Munster!

    Running: Check out a great running website.