Vertex-based finite volume simulation of Liesegang patterns on structureless meshes

A computational method is suggested for the simulation of Liesegang patterns in two dimensions on structureless meshes. The method is based on a model that incorporates dynamical equations for the nucleation and growth of solid particles of different sizes into reaction-diffusion equations. We find the model cannot be numerically solved with Galerkin-based finite element methods and cell-centered finite volume methods. Instead, the vertex-based finite volume method is used to correctly reproduce the Liesegang pattern on structureless meshes. The numerical solution is then compared with specially designed experiments on Liesegang patterns in various geometries, and it is shown to be in good agreement.