Coupled Level-Set Lattice Boltzmann Method on Adaptive Cartesian Grids

TL;DR

The paper tackles the challenge of accurately simulating liquid–gas multiphase flows with sharp interfaces and large density ratios by proposing a fully coupled two-fluid framework on adaptive Cartesian grids. Each phase is solved with its own numerical algorithm on a shared hierarchical grid, while a level-set description tracks the interface and a modified bounce-back boundary enforces continuity and jump conditions at the interface. Key contributions include enabling independent per-phase solvers (e.g., BGK for liquid and cumulant for gas), a novel non-equilibrium refilling strategy for newly activated cells, and AMR driven by solver-specific sensors to concentrate resolution near interfaces and steep gradients. Validation on laminar stratified flows, single rising bubbles, and a cluster of bubbles demonstrates high-fidelity results and notable efficiency gains from AMR, highlighting the method’s potential for complex interfacial dynamics in multiphase systems.

Abstract

A novel coupled level-set lattice Boltzmann method on adaptive Cartesian grids for simulating liquid-gas multiphase flows is presented. The approach addresses the inherent challenges of accurately modeling multiphase systems characterized by sharp interfaces and large density ratios. By employing separate solution algorithms for each fluid phase which are coupled through boundary conditions at the interface the method is more accurate and more efficient. The study highlights the advantages of using lattice Boltzmann methods together with level-set techniques to track interfaces effectively while facilitating adaptive mesh refinement. Applications to various test cases, e.g., immiscible stratified flow and rising bubbles, demonstrate the method's capability to capture complex interfacial dynamics and validate its accuracy against literature data.

Figures (10)

• Figure 1: Velocity space discretization in two and three dimensions.
• Figure 2: Interface description using the level-set (a). Missing distributions for both lattice Boltzmann solvers (/) (b). Intersection between distributions and the interface are marked with .
• Figure 3: Example configuration illustrating the level set sweeping over a grid node $\vec{x}_r$ () during one time step $\Delta t$ such that it becomes an active node in $\Omega_1$ and inactive in $\Omega_2$, i.e., the associated level-set value at $\varphi(\vec{x}_r)$ switches sign. The interface normal $\vec{n}$ as well as the closest lattice direction $\vec{e}_{min}$ are shown.
• Figure 4: Example cutout of a parallel quad tree data structure for a two-dimensional hierarchical Cartesian grid. The LS solver is active on all leaf-cells , i.e., cells on the maximum refinement level, while both flow solvers are only active together in the cells where the interface is present . In the bulk of the respective fluid domains, only the corrsesponding LB gas or LB liquid solver is active /. Here, two subdomains for the parallelization as shown.
• Figure 5: Velocity profiles for different stratified two-phase flows for a viscosity ratio $\eta_1/\eta_2=10$.