An Application of the Cahn-Hilliard Approach to Smoothed Particle Hydrodynamics

The development of a methodology for the simulation of structure formingprocesses is highly desirable. The smoothed particle hydrodynamics (SPH)approach provides a respective framework for modeling the self-structuringof complex geometries. In this paper, we describe a diffusion-controlledphase separation process based on the Cahn-Hilliard approach using theSPH method. As a novelty for SPH method, we derive an approximationfor a fourth-order derivative and validate it. Since boundary conditionsstrongly affect the solution of the phase separation model, we apply boundaryconditions at free surfaces and solid walls. The results are in good agreementwith the universal power law of coarsening and physical theory. It is possibleto combine the presented model with existing SPH models