[C18] Biomathematics

[C18-01] Unconditionally energy gradient stable, linear scheme for tissue growth model using phase field and chemotaxis models

*Gyeonggyu Lee¹, Seunggyu Lee (1. National Institute of Mathematical sciences (Korea))

Keywords:

Tissue growth model,Phase field model,Convex splitting method

In this presentation, we consider the phase field and chemotaxis models for modelling tissue growth. To construct the governing equation, we use the Cahn-Hilliard equation to describe cell fracture. The relation between cells and nutrients is modeled using the chemotaxis model. The source term of the modified Cahn-Hilliard equation is constructed using a chemical reaction network. The total energy dissipation and mass preservation properties are confirmed. To numerically solve the governing equation, we use the convex splitting method. Splitting the Lyapunov function into contractive and expansive parts, we can construct the unconditionally energy gradient stable scheme using the convexity of the contractive and expansive parts. We validate the energy gradient stability and mass preservation property from the numerical analysis and experiment. Moreover, we demonstrate the unique solvability of the proposed numerical scheme using block LU decomposition and eigenvalues of each operator.