Scientific article
Open access

Numerical approximation of a 3D mechanochemical interface model for skin patterning

Published inJournal of computational physics, vol. 384, p. 383-404
Publication date2019-05

We introduce a model for the mass transfer of molecular activators and inhibitors in two media separated by an interface, and study its interaction with the deformations exhibited by the two-layer skin tissue where they occur. The mathematical model results in a system of nonlinear advection-diffusion–reaction equations including cross-diffusion, and coupled with an interface elasticity problem. We propose a Galerkin method for the discretisation of the set of governing equations, involving also a suitable Newton linearisation, partitioned techniques, non-overlapping Schwarz alternating schemes, and high-order adaptive time stepping algorithms. The experimental accuracy and robustness of the proposed partitioned numerical methods is assessed, and some illustrating tests in 2D and 3D are provided to exemplify the coupling effects between the mechanical properties and the advection-diffusion–reaction interactions involving the two separate layers.

  • Elasticity-diffusion problem
  • Interface coupling
  • Pattern formation
  • Skin appendage modelling
  • Finite element methods
  • Adaptive time stepping
  • UK Research and Innovation - Conservative methods for poroelasticity [EP/R00207X/1]
Citation (ISO format)
DE OLIVEIRA VILACA, Luis Miguel, MILINKOVITCH, Michel C., RUIZ-BAIER, Ricardo. Numerical approximation of a 3D mechanochemical interface model for skin patterning. In: Journal of computational physics, 2019, vol. 384, p. 383–404. doi: 10.1016/j.jcp.2019.01.023
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Article (Published version)
ISSN of the journal0021-9991

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