Numerical method for the bone regeneration model, defined within the evolving 2D axisymmetric physical domain

► Direct bone apposition on a pre-existing surface is modeled. ► Advection-diffusion-reaction equations are solved numerically within evolving domain. ► Finite volume approach on the evolving in time 2D unstructured grid is constructed. ► Exact Riemann solution is found for the nonlinearly coupled system of equations. ► Different osseointegration modes are predicted for smooth and micro-rough implants.