Speaker
Description
The pseudopotential method [Shan, Chen (1993), https://doi.org/10.1103/PhysRevE.47.1815] is a popular multiphase extension to the lattice Boltzmann method (LBM). Several improvements to the method have been proposed, allowing for better thermodynamic consistency, surface tension control, or stability for high density ratios [Czelusniak et al. (2020), https://doi.org/10.1103/PhysRevE.102.033307]. However, pseudopotential LBMs are rarely tested for grid convergence, which is essential in complex applications.
The pseudopotential method is a diffuse interface approach, where the interface has a finite thickness, and the balance equations for mass, momentum, and energy are applied in this region with additional terms. Discretization errors can significantly impact results near the interface, making the use of finer grids critical. In general, grid convergence of pseudopotential LBMs is conducted in two approaches, which can be distinguished with the help of the Cahn number Ch. The first refinement principle increases the total number of grid nodes N along with the number of grid nodes at the interface W, approaching the continuous diffuse interface solution, i.e. Ch=W/N=constant. The second refinement principle increases N, but keeps W constant, that is, Ch approaches 0. The latter reduces the thickness of the physical interface, so that the solution should approach a sharp interface. In this work, we focus on the first principle (Ch=constant) and discuss how to achieve consistency in the case of a diffuse interface. Our approach is based on keeping the pressure tensor invariant in physical units for different resolutions.
With our strategy, we are able to validate the second-order accuracy of the pseudopotential LBM in several benchmarks, such as a planar interface flow, a static droplet simulation, and a two-phase flow between parallel plates. In addition, we also use our procedure to validate the second-order accuracy of the pseudopotential LBM in application-relevant benchmark problems, such as the impact of a droplet on solid and structured surfaces. All test cases are implemented in the parallel open-source library OpenLB [Krause et al. (2021), https://doi.org/10.1016/10.1016/j.camwa2020.04.033].
In conclusion, our proposed validation strategy will be essential for establishing the usage of efficient LBM in industrial simulations to develop technologies such as waterproof surfaces [Evans, Bryan (1999), https://doi.org/10.1016/S0007-8506(07)63233-8] or to improve the heat exchange efficiency of droplet evaporation [Misyura et al. (1999), https://doi.org/10.1016/j.ijheatmasstransfer.2022.122843].
