A conservative and variation preserving finite volume method for non-overlapping meshes of reaction and diffusion in angiogenesis

• Reaction and diffusion of growth factors in angiogenesis.
• Reaction and the diffusion meshes are non-overlapping.
• Conservative and reaction-variation preserving finite volume method.
• Handle non-uniform discretization and arbitrary shaped reaction domains.

We propose a conservative and variation preserving finite volume method for reaction and diffusion in angiogenesis. The reaction domain keeps changing the morphology and length, and its mesh is non-uniform and does not overlap with the diffusion mesh. These facts make it very challenging to develop a numerical method that conserves the mass when transferring data between the reaction and diffusion domains. We prove the method developed in this work not only conserves the mass locally but also retains the variation in the reaction domain. In contrast, the direct interpolation may smear out the reaction data in the data transfer process. This method is applied to the growth factor reaction and diffusion problems in angiogenesis.