ArticleJournal of computational physics2014
A conservative algorithm for parabolic problems in domains with moving boundaries.
Article in Journal of computational physics, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry.Molecular biology of the cell · 2021Article
- A Review of Cell-Based Computational Modeling in Cancer Biology.JCO clinical cancer informatics · 2019Review
- A free-boundary model of a motile cell explains turning behavior.PLoS computational biology · 2017Article
- A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.Proceedings. Mathematical, physical, and engineering sciences · 2017Article
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2 authors.
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Abstract
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.
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