Adjustable surface tension independent of the collision operator for pseudopotential lattice Boltzmann methods

In this work, we propose an alternative surface tension adjustment approach in the pseudopotential lattice Boltzmann (LB) model, which is not only decoupled from the density ratio but also independent of the collision operator. This is achieved by incorporating a generic source term obtained from the difference between a modified moment equilibrium and an original moment equilibrium distribution function in the LB equation. The explicit form of the source term is obtained through a third-order Chapman-Enskog analysis of the LB equation, aiming to recover the targeted governing equations from a modified Landau free-energy theory using a hybrid density-pseudopotential form. The source term can be easily and straightforwardly incorporated into different widely used collision operators, such as single relaxation time, multiple relaxation time and entropic-MRT operators. The proposed method is validated by three benchmarks: (i) the liquid-gas coexistence density, (ii) surface tension adjustment via the static droplet case, and (iii) droplet deformation via oscillations. It is shown that thermodynamic consistency is restored in a large range of temperature ratio, and, moreover, a remarkable tunable surface tension range of 140 times can be achieved. Benefiting from the proposed surface tension adjustment method, we have successfully modeled the droplet impact and splashing dynamics with a Weber number up to 10 500, achieving one order of magnitude higher than LB simulations reported in the literature.