Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 270, Issue -, Pages 203-213Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.03.014
Keywords
Numerical algorithm; Moving boundaries; Parabolic equations; Exact mass conservation; Cell migration
Funding
- National Institutes of Health, through grants from the National Center for Research Resources, NIH [2P41RR013186-15]
- National Institute of General Medical Sciences, NIH [9P41GM103313-15, U54GM64346]
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We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. Numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward. Published by Elsevier Inc.
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