Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Lavrentyev prosp. 15, 630090 Novosibirsk, Russia.
Novosibirsk State University, Pirogova str. 2, 630090 Novosibirsk, Russia.
Phys Rev E. 2018 Aug;98(2-1):023308. doi: 10.1103/PhysRevE.98.023308.
An alternative method to simulate heat transport in the multiphase lattice Boltzmann (LB) method is proposed. To solve the energy transport equation when phase boundaries are present, the method of a passive scalar is considerably modified. The internal energy is represented by an additional set of distribution functions, which evolve according to an LB-like equation simulating the transport of a passive scalar. Parasitic heat diffusion near boundaries with a large density gradient is suppressed by using special "pseudoforces" which prevent the spreading of energy. The compression work and heat diffusion are calculated by finite differences. A new method to take into account the latent heat of a phase transition Q(T) is realized. The latent heat is released or absorbed continuously inside a thin transition layer in a certain range of density, ρ_{1}<ρ<ρ_{2}. This allows one to avoid interface tracking. Several tests were carried out concerning all aspects of the processes. It is shown that the Galilean invariance and the scaling of the thermal conduction process hold, as well as the correct dependence of the sound speed on the heat capacity ratio. The method proposed has low scheme diffusion of the internal energy, and it can be applied to modeling a wide range of multiphase flows with heat and mass transfer even for high density ratios of liquid and vapor phases.
提出了一种模拟多相格子玻尔兹曼（LB）方法中热传递的替代方法。为了解决存在相界面时的能量传递方程，对被动标量的方法进行了相当大的修改。通过使用特殊的“伪力”来抑制边界处具有大密度梯度的寄生热扩散，内部能量由一组附加的分布函数表示，这些分布函数根据类似于 LB 的方程演变，模拟被动标量的传输。通过有限差分计算压缩功和热扩散。实现了一种新的方法来考虑相变潜热 Q(T)。在密度ρ_{1}<ρ<ρ_{2}的一定范围内，潜热在薄过渡层内连续释放或吸收。这可以避免界面跟踪。针对这些过程的各个方面进行了多项测试。结果表明，伽利略不变性和热传导过程的比例缩放以及声速对热容比的正确依赖性得以保持。所提出的方法具有较低的内部能量方案扩散，可以应用于模拟具有热质量传递的多种相流，即使在液相和气相的密度比很高的情况下也是如此。
