Discrete methods of the energy equations in the pseudo-potential lattice Boltzmann model based simulations

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid-vapor phase change

“…To treat the liquid-vapor phase change problem, the above governing equation is usually rewritten as a standard convection-diffusion equation in previous LB models [21,22,32], such that a discrete source term related to ∇ (ρc v ) was also needed to be added into the temperature evolution, which may affect the numerical stability and accuracy when the fluid properties change significantly across the liquid-vapor interface [24,25]. In this setting, recently we proposed a 2D MRT thermal LB model for liquid-vapor phase change [33], and in contrast to previous LB models, the calculation of ∇ (ρc v ) is eliminated in the proposed model.…”

“…Although some thermal LB models have been constructed to simulate liquid-vapor flows with phase change, there exist two primary defects in these approaches. To begin with, to recover the correct energy equation, the source terms used in these models contain the gradient term of ∇ (ρc v ) (here, ρ is the fluid density and c v is the specific heat at constant volume), which may bring some additional errors when the fluid properties across the liquid-vapor interface are significantly different [24,25], and meanwhile, this treatment also increases the computational load in the practical simulations, and this phenomenon is more distinct for 3D cases. Secondly, all the mentioned thermal LB models are constructed for the two-dimensional (2D) cases.…”

2D Simulation of boiling heat transfer on the wall with an improved hybrid lattice Boltzmann model

“…The gradient of the thermal conductivity loses its mathematical rigor as the width of the interface is 0 in this case. To maintain the energy conservation, in our previous work [4], a 1th order discretion scheme is applied in the term of    …”

“…Besides of the experimental method, numerical simulations are also widely applied in the studying of the flow and heat transfer problem. Bubble growth and boiling heat transfer can be simulated by coupling the multi-phase flow models [4][5][6][7][8] with the energy equations [9,10]. Among these multi-phase models, the lattice Boltzmann (LB) method [11] based models are most promising.…”