Modelling time-dependent partial differential equations using a moving mesh approach based on conservation

Host Institution:

La Trobe University 

Title of Seminar:

Modelling time-dependent partial differential equations using a moving mesh approach based on conservation

Speaker's Name:

Dr Tamsin E. Lee

Speaker's Institution:

University of Reading, UK

Time and Date:

Friday 22 March, 2.00 PM (AEDT)

Seminar Abstract:

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. 

Seminar Convenor:

 

This email address is being protected from spambots. You need JavaScript enabled to view it.

 

AGR IT support:

This email address is being protected from spambots. You need JavaScript enabled to view it. This email address is being protected from spambots. You need JavaScript enabled to view it.