Abstract In this work, a double-MRT lattice Boltzmann (LB) model for thermal multiphase flow is presented and analyzed. The model is based on a pseudopotential scheme, and introduces a second equation with a non-diagonal relaxation matrix and an explicit definition of the equilibrium distribution in moment space. This alternative approach formally reproduces the target energy equation with no additional terms up to the relevant expansion scale, avoiding traditional explicit corrections in the source term or post-collision distributions. It also preserves the parallelization properties of the algorithm and proves that it can accurately simulate numerical tests with known analytical solutions, namely density and temperature distribution in a stratified van der Waals fluid, and interface evolution in a Stefan flow problem. Furthermore, a two-step grid independency test with fixed dimensionless numbers was analyzed and successfully applied in the simulation of bubble generation on a heated horizontal plate, showing that this methodology can be performed to prove consistency and order of convergence of the resulting LB scheme. For this particular problem, the influence of boundary conditions and numerical treatment of non-local terms in the energy equation are discussed in detail.

中文翻译：

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用于多相流和传热模拟的双 MRT 赝势晶格 Boltzmann 模型的评估

摘要 在这项工作中，提出并分析了热多相流的双 MRT 晶格玻尔兹曼 (LB) 模型。该模型基于赝势方案，并引入了具有非对角松弛矩阵的第二个方程和力矩空间中平衡分布的明确定义。这种替代方法在没有附加项的情况下正式再现了目标能量方程，直到相关扩展规模，避免了源项或碰撞后分布中的传统显式校正。它还保留了算法的并行化特性，并证明它可以使用已知解析解准确模拟数值测试，即分层范德华流体中的密度和温度分布，以及 Stefan 流问题中的界面演化。此外，分析了具有固定无量纲数的两步网格独立性测试并成功应用于加热水平板上气泡生成的模拟，表明该方法可以用来证明所得 LB 方案的一致性和收敛顺序。对于这个特殊问题，详细讨论了边界条件的影响和能量方程中非局部项的数值处理。