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首页> 外文期刊>International Journal of Heat and Mass Transfer >An implicit lattice Boltzmann model for heat conduction with phase change
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An implicit lattice Boltzmann model for heat conduction with phase change

机译：相变热传导的隐式格子玻尔兹曼模型

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摘要

In this work, a new variation of the lattice Boltzmann method (LBM) was developed to solve the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term was treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The Bhatnagar-Gross-Krook (BGK) approximation with a D2Q9 lattice was applied and different boundary conditions including Dirichlet and Neumann boundary conditions were considered. The developed model was tested by solving a one-dimensional melting problem for a pure metal, and one and two-dimensional solidification problems for a binary alloy. The results of the LBM solution were compared with analytical and finite element solutions and a good consistency was observed. Considering the special capabilities that LBM offers, like local characteristic, and inherent parallel structure, the developed model is an interesting alternative to traditional continuum models.
机译：在这项工作中，开发了一种新的格子玻尔兹曼方法（LBM）来解决具有相变的热传导问题。与以前的显式算法相比，潜热源项在能量方程中被隐式处理，从而避免了迭代步骤并提高了配方的稳定性和效率。应用具有D2Q9格的Bhatnagar-Gross-Krook（BGK）近似，并考虑了包括Dirichlet和Neumann边界条件在内的不同边界条件。通过解决纯金属的一维熔化问题以及二元合金的一维和二维凝固问题，测试了开发的模型。将LBM解的结果与解析解和有限元解进行了比较，并观察到了良好的一致性。考虑到LBM提供的特殊功能（例如局部特征和固有的并行结构），开发的模型是传统连续模型的有趣替代方案。

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