A numerical approach for coupling the Lattice Boltzmann Method with a membrane finite element to simulate surface tension driven dynamics in 2D

  • Séguy, François (Ecole Centrale de Lyon, LTDS)
  • Valette, Stéphane (Ecole Centrale de Lyon, LTDS)
  • Bocher, Philippe (École De Technologie Supérieure ÉTS)
  • Lévêque, Emmanuel (Ecole Centrale de Lyon, LMFA)
  • Feulvarch, Eric (Ecole Centrale de Lyon, LTDS)

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Numerical simulation of multiphase flows and wettability phenomena represents a significant industrial and scientific challenge in fields such as surface functionalization. To model these complex interfaces, the Lattice Boltzmann Method (LBM) has emerged as an efficient approach to simulate fluid dynamics at a mesoscopic scale. One popular multiphase approach is the Shan-Chen pseudo-potential model. However, this model has intrinsic limitations in configurations with high density ratios, such as wettability simulations approaching 1000:1 ratios in liquid-gas interactions. These limitations cause instabilities in surface tension forces and undesirable 'spurious currents' phenomena. The aim of this work is to introduce a method for coupling the LBM with a membrane finite element developped by Feulvarch et al. This model is a Lagrangian method that allows for defining boundary conditions for the fluid domain by tracking the air-liquid interface. Assuming that the evolution of this interface is primarily driven by the normal effect of surface tension, it is possible to construct a geometry by simulating only an external membrane. Fluid-structure couplings using FEM and LBM formulations have already been studied by considering low couplings. One extension of the LBM that facilitates this coupling is the Immersed Boundary Method (IBM) and adapted to the specificities of the LBM. The idea is to add Lagrangian markers to the Eulerian LBM grid, which evolve according to the fluid dynamics. In this work, a high coupling level is proposed to simulate the membrane dynamics that evolves according to the fluid pressure computed in the LBM simulation. Then, according to the IBM scheme, the moving boundary at the next time step drives the fluid flow that allows a new pressure to be computed. The algorithm seeks an equilibrium between the LBM computed pressure and the nodal pressure computed by the membrane finite element.