Assessment of a double-MRT pseudopotential lattice Boltzmann model for multiphase flow and heat transfer simulations

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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.