A Finite Volume Spatial Discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing

We consider the numerical simulation of a time-dependent taxis-diffusion-reaction
model of fracture healing in mice using the method of lines. The partial differential equation problem has an axi-symmetric structure and this is employed to properly reduce the model to an equivalent problem in two-dimensional (2D) space leading subsequently to an efficient spatial discretisation. Special care is given to respect conservation of mass and the non-negativity of the solution. The numerical simulation results are contrasted to those obtained from a simplistic reduction of the axi-symmetric model to 2D space (at the same computational cost).We observe quantitative and qualitative differences.