An operator splitting method for the Cahn–Hilliard equation on nonuniform grids

In this study, we present an operator splitting method (OSM) for the Cahn–Hilliard (CH) equation on a nonuniform mesh. The CH equation is a fourth-order partial differential equation that models phase separation phenomena in binary mixtures. Because the CH equation is applied in various scientific fields, numerous numerical methods have been developed to enhance the computational efficiency and accuracy. In this work, we consider a nonuniform mesh to improve spatial efficiency. To solve the CH equation in two-dimensional (2D) space on a nonuniform mesh, we consider the linear stabilized splitting (LSS) scheme along with the OSM. The LSS scheme is an unconditionally energy gradient stable method. To construct a simple numerical scheme, we consider the OSM in two-dimensional space. We validate that the proposed scheme satisfies the mass-preserving property. Furthermore, we conduct numerical experiments to demonstrate the efficiency and various properties of the proposed scheme.