A High-Order Finite Volume Method for the Simulation of Phase Transition Flows Using the Navier–Stokes–Korteweg Equations

In this work, we employ the Navier–Stokes–Korteweg system of equations for the simulation of phase transition flows. This system belongs to the diffuse interface models, in which both phases are separated by a non-zero thickness interface where the properties vary continuously. The key idea of these methods is the ability to use the same set of equations for the entire computational domain, regardless of the phase of the fluid. However, these methods lead to a system of equations with high-order derivatives, which are difficult to discretize and solve numerically. Here, we propose the use of a high-order Finite Volume method, FV-MLS, for the resolution of the Navier–Stokes–Korteweg equations. The method uses Moving Least Squares approximations for the direct and accurate discretization of higher-order derivatives, which is particularly suitable for simulations on unstructured meshes. In this work, we show two numerical examples in which the interface is set to interact with great changes in the properties, in order to demonstrate the robustness of the method.