SMS scnews item created by Andrew Mathas at Thu 14 Mar 2013 1107
Expiry: 22 Mar 2013
Calendar1: 22 Mar 2013 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: AGR Seminar: Modelling time-dependent partial differential equations using a moving mesh approach based on conservation
Auth: firstname.lastname@example.org (assumed)
Modelling time-dependent partial differential equations using a moving mesh approach based on conservation
Dr Tamsin E. Lee (University of Reading, UK)
La Trobe University
One of the advantages of moving mesh methods for the numerical solution of partial differential equations is their ability to track moving boundaries. In this talk we propose a velocity-based moving mesh method in which we primarily focus on moving the nodes so as to preserve local mass fractions. To recover the solutions from the mesh we use an integral approach which avoids altering the structure of the original equations when incorporating the velocity. We apply our method to a range of moving boundary problems: the porous medium equation; Richards' equation; the Crank-Gupta problem; an avascular tumour growth model. We compare the numerical results to exact solutions where possible, or to results obtained from other methods, and find that our approach is accurate. We apply three different strategies to the tumour growth model, which enables us to make comparisons between the different approaches. We conclude that our moving mesh method can offer equal accuracy and better resolution, whilst offering greater flexibility than a standard fixed mesh approach.
Dr Yury Nikolayevsky
If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to email@example.com to let the CSOs know that you would like to attend.