A Lagrangian particle method for reaction-diffusion systems on deforming surfaces.
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.
Bergdorf
Michael
M
Department of Computational Science, ETH Zurich, Zurich, Switzerland.
Sbalzarini
Ivo F
IF
Koumoutsakos
Petros
P
D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D036341:Intercellular Signaling Peptides and Proteins / Q000378:metabolism*; D008954:Models, Biological; D009024:Morphogenesis / Q000502:physiology*; D009369:Neoplasms / Q000098:blood supply / Q000473:pathology; D009389:Neovascularization, Pathologic / Q000473:pathology; D013499:Surface Properties
D036341:Intercellular Signaling Peptides and Proteins