Abstract
Reaction–diffusion processes on complex deforming surfaces are fundamental to a number of biological processes ranging from embryonic development to cancer tumor growth and angiogenesis. The simulation of these processes using continuum reaction–diffusion models requires computational methods capable of accurately tracking the geometric deformations and discretizing on them the governing equations. We employ a Lagrangian level-set formulation to capture the deformation of the geometry and use an embedding formulation and an adaptive particle method to discretize both the level-set equations and the corresponding reaction–diffusion. We validate the proposed method and discuss its advantages and drawbacks through simulations of reaction–diffusion equations on complex and deforming geometries.
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Bergdorf, M., Sbalzarini, I.F. & Koumoutsakos, P. A Lagrangian particle method for reaction–diffusion systems on deforming surfaces. J. Math. Biol. 61, 649–663 (2010). https://doi.org/10.1007/s00285-009-0315-2
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DOI: https://doi.org/10.1007/s00285-009-0315-2