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

Abstract

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°–1.52° 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.