Sarah
Mitchell's home page

Sarah Mitchell (MMath, Ph.D)
 Position:
 Head of Department & Senior Lecturer in
Applied Mathematics
 Address:
 Department
of Mathematics & Statistics (D2033)
University of Limerick
Limerick
Ireland  Telephone Number:
 +35361202259
 Fax:

+35361334927
 Email:
 sarah.mitchell@ul.ie
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 fluiddriven) fractures in rocks. This is joint work with Prof. Anthony Peirce from the University of British Columbia, Vancouver.
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 uptodate copy of my CV can be found here and below is a list of my publications:
M. Vynnycky, S.L. Mitchell, "On the numerical solution of a Stefan problem with finite extinction time", Journal of Computational and Applied Mathematics, 276, 98109, 2015.
S.L. Mitchell, M. Vynnycky, "The oxygen diffusion problem: analysis and numerical solution", Applied Mathematical Modelling, 39, 27632776, 2015.
S.L. Mitchell, "Applying the combined integral method to twophase Stefan problems with delayed onset of phase change", Journal of Computational and Applied Mathematics, 281, 5873, 2015.
F. Font, T.G. Myers, S.L. Mitchell, "A mathematical model for nanoparticle melting with density change", Microfluid Nanofluid, 18, 233243, 2015.
M. Vynnycky, S.L. Mitchell, B.J. Florio, S.B.G. O'Brien, "Decoupling the interaction of solid and fluid mechanics in the modelling of continuous casting processes", Progress in Industrial Mathematics at ECMI 2014, in press.
S.L. Mitchell, S.B.G. O'Brien, "The two envelope problem: there is no conundrum", Teaching Mathematics and its Applications, doi:10.1093/teamat/hru019, 2014.
L.B. Cribbin, H.F. Winstanley, S.L. Mitchell, A.C. Fowler, G.C. Sander, "Reaction front formation in contaminant plumes", Journal of Contaminant Hydrology, 171, 1221, 2014.
S.L. Mitchell, "An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue", Applied Mathematical Modelling, 38, 43964408, 2014.
S.L. Mitchell, S.B.G. O'Brien, "Asymptotic and numerical solutions of a free boundary problem for the sorption of a finite amount of solvent into a glassy polymer", SIAM Journal on Applied Mathematics, 74(3), 697723, 2014.
S.L. Mitchell, M. Vynnycky, "On the numerical solution of twophase Stefan problems with heatflux boundary conditions", Journal of Computational and Applied Mathematics, 264, 4964, 2014.
N.A.S. Smith, S.L. Mitchell, A. Ramos, "Analysis and Simplification of a Mathematical Model for HighPressure Food Processes", Applied Mathematics and Computation, 226, 2037, 2013.
M. Vynnycky, S. L. Mitchell, "On the Accuracy of a FiniteDifference Method for Parabolic PDEs with Discontinuous Boundary Conditions", Numerical Heat Transfer, Part B, 64, 275292, 2013.
M. Vynnycky, W. T. Lee, S. L. Mitchell, G. Richardson, "Foam formation in the plastics industry", MathematicsinIndustry Cast Studies Journal, 5, 2742, 2013.
F. Font, S. L. Mitchell, T. G. Myers. "Onedimensional solidification of supercooled melts", International Journal of Heat and Mass Transfer, 62, 411421, 2013.
T. G. Myers, S. L. Mitchell, "A mathematical analysis of the motion of an inflight soccer ball", Sports Engineering, 16, 2941, 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, 376388, 2012.
S. L. Mitchell, T. G. Myers, "Application of heat balance integral methods to onedimensional 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 onephase supercooled Stefan problem", International Communications in Heat and Mass Transfer, International Communications in Heat and Mass Transfer, 39, 15221525, 2012.
S. L. Mitchell, M. Vynnycky, "An accurate finitedifference method for ablationtype Stefan problems", Journal of Applied and Computational Mathematics, 236, 41814192, 2012.
S. L. Mitchell, "Applying the combined integral method to onedimensional ablation", Applied Mathematical Modelling, 36, 127138, 2012.
S. L. Mitchell, "An accurate nodal heat balance method with spatial subdivision", Numerical Heat Transfer, Part B, 60, 3456, 2011.
T. G. Myers, S. L. Mitchell, "Application of the Combined Integral Method to Stefan problems", Applied Mathematical Modelling, 35, 42814294, 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, 92199233, 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, 35403551, 2010.
S. L. Mitchell, T. G. Myers, "Application of Standard and Refined Heat Balance Integral Methods to OneDimensional Stefan Problems", SIAM Review, 52(1), 5786, 2010.
M. Vynnycky, S. L. Mitchell, "Evaporative cooling and the Mpemba effect", Heat and Mass Transfer, 46, 881890, 2010.
T. G. Myers, S. L. Mitchell, "Mathematical Modelling of Phase Change with a Flowing Thin Film", Progress in Industrial Mathematics at ECMI 2010, 399405.
S. L. Mitchell, "Approximate solution methods for the onedimensional 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 phasechange", 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, July 2010.
S. L. Mitchell, M. Vynnycky, "Finitedifference methods with increased accuracy and correct initialization for onedimensional Stefan problems", Applied Mathematics and Computation, 215, 16091621, 2009.
T. G. Myers, S. L. Mitchell, "Application of the heat balance and refined heat balance integral methods to the Kortewegde Vries equation", Thermal Science, 13(2), 112119, 2009.
T. G. Myers, S. L. Mitchell, G. Muchatibaya, "Unsteady contact melting of a rectangular crosssection phase change material", Physics of Fluids, 20 (103101), 2008.
S. L. Mitchell, T. G. Myers, "Heat Balance Integral Method for OneDimensional Finite Ablation", AIAA Journal of Thermophysics and Heat Transfer, 22(3), 508514, 2008.
S. L. Mitchell, T. G. Myers, "Approximate solution methods for onedimensional solidification from an incoming fluid", Applied Mathematics and Computation, 202(1), 311326, 2008.
T. G. Myers, S. L. Mitchell, G. Muchatibaya, M. Y. Myers, "A cubic heat balance integral method for onedimensional melting of a finite thickness layer", International Journal of Heat and Mass Transfer, 50, 53075315, 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, 365372, 2007.
S. L. Mitchell, R. Kuske, A. P. Peirce, "An asymptotic framework for finite hydraulic fractures including leakoff", SIAM Journal on Applied Mathematics, 67(2), 364386, 2007.
S. L. Mitchell, T. G. Myers, "The laminarturbulent 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), 12021225, 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.