Combining lattice Boltzmann and smoothed profile methods for calculating the interface normal vectors and its application for simulating dissolution phenomenon

The method of volume of fluid is a popular method often used to calculate normal vectors in simulating two-phase flows. This study proposes a new method based on scalar diffusion phenomenon using smoothed profile combined with lattice Boltzmann method. The method is spatially and time-wisely local, which facilitates its parallel implementation. Accuracy and computational time of the proposed method on straight and curved surfaces in single-and multi-obstacle media were compared with four standard methods: Youngs, efficient least-square volume of fluid interface reconstruction algorithm (ELVIRA), Swartz, and coupled volume of fluid and level set (VOSET). In addition, the problems of heterogeneous dissolution of porous media under reaction-controlled and natural conditions were simulated. The results showed that in terms of the calculated angles, the proposed method is 0.4 degrees-1.52 degrees more accurate than the common Youngs method. Additionally, its computational time was about 36% less than that of the Youngs method. Compared with ELVIRA, Swartz, and VOSET, despite their marginal higher accuracy, their computational times were 346%-772% higher. Furthermore, it was shown that the accuracy of ELVIRA and Swartz methods in multi-obstacle media decreases significantly with decrease in gap between the neighboring obstacles. However, for the proposed method, the effect of gap was considerably less significant.

Automated summary

This study proposes a new method based on scalar diffusion phenomenon combined with lattice Boltzmann method to calculate normal vectors in simulating two-phase flows. The proposed method is more accurate and computationally efficient compared to standard methods such as Youngs, ELVIRA, Swartz, and VOSET. It is also less affected by the gap between neighboring obstacles in multi-obstacle media.