Interface Capturing Method Based on the Cahn–Hilliard Equation for Two-Phase Flows

A numerical method for flows of heterogeneous two-phase compressible media is considered. The main problem in the construction of such a method is to find the interface between the components with different physical and mechanical properties. An efficient method for solving this problem that gives a good spatial resolution of the interfaces is proposed. This method is based on the use of the Cahn–Hilliard equation. To describe the flow of the two-phase medium, the single-velocity five-equation model is used; in this model, the Cahn–Hilliard equation is used as the equation for the order function. This makes it possible to significantly decrease the domain of the interface numerical smearing. Numerical results confirm the high accuracy and effectiveness of the proposed method.