A Lagrangian particle method for reaction–diffusion systems on deforming surfaces
Bergdorf M., Sbalzarini I. F., Koumoutsakos P., Journal of Mathematical Biology, 61, 5, 649-663, 2010
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.