Lattice Boltzmann Model for Axisymmetric Multiphase Flows

A novel lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynami...

The pseudopotential method is one of the most popular extensions of the lattice Boltzmann method (LBM) for phase change and multiphase flow simulation. One attractive feature of the original proposed method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function, which became known as the Shan-Chen interaction force. Some of the well known drawbacks implied by this method involves lack of thermodynamic consistency and impossibility to c...

We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are recovered in the hydrodynamic limit. A scaling based on the smallness of velocity increments is then introduced, which recovers the full Navier-Stokes-Korteweg equations. The proposed model is realized on a standard lattice and validated on...

We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021). While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and Courant--Friedrichs--Lewy number. Here we show that the entropi...

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case...

A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three sub-operators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu--Valocchi--Kang perturbation operator, and a Latva-Kokko--Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also inco...

This study compares the free-surface lattice Boltzmann method (FSLBM) with the conservative Allen-Cahn phase-field lattice Boltzmann method (PFLBM) in their ability to model two-phase flows in which the behavior of the system is dominated by the heavy phase. Both models are introduced and their individual properties, strengths and weaknesses are thoroughly discussed. Six numerical benchmark cases were simulated with both models, including (i) a standing gravity and (ii) capil...

The lattice Boltzmann method is adopted to solve the liquid-vapor phase change problems in this article. By modifying the collision term for the temperature evolution equation, a new thermal lattice Boltzmann model is constructed. As compared with previous studies, the most striking feature of the present approach is that it could avoid the calculations of both the Laplacian term of temperature [$\nabla \cdot \left( {\kappa \nabla T} \right)$] and the gradient term of heat ca...

We present high resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a Lattice Boltzmann method. We first validate the thermodynamical and kinematical properties of the algorithm. Then, we perform a series of 3d numerical simulations at changing the mean properties in the phase diagram and compare convection with and without phase coexistence at $Ra \sim 10^7$. We show that in presence of nucleating bubbles non-Oberbeck...

In the classical multiple-relaxation-time (MRT) lattice Boltzmann (LB) method, the transformation matrix is formed by constructing a set of orthogonal basis vectors. In this paper, a theoretical and numerical study is performed to investigate the capability and efficiency of a non-orthogonal MRT-LB model for simulating multiphase flows. First, a three-dimensional non-orthogonal MRT-LB is proposed. A non-orthogonal MRT collision operator is devised based on a set of non-orthog...