Abstract: Liquid-liquid miscible interaction phenomena are ubiquitous in our everyday lives, while it is very difficult to simulate due to the complicated interaction process.In the paper, a volume function based method is proposed to simulate the liquid-liquid miscible interaction.In the method, the fluid equations are solved using a second order accurate finite volume method, and the miscible mutual interaction between different liquids is simulated through tracking the volume function of each liquid component in each grid cell.The computation is accelerated with an octree-based adaptive mesh refinement algorithm.The experiments show that the presented method is stable and can generate results with rich diffusion details.