A double-population lattice Boltzmann method is applied to simulate the convectiondiffusion phenomena associated with solid-liquid phase transition processes. The research focus is the lattice Boltzmann method advanced to complex multitube heat storage system with different numbers and arrangements of tubes. A systematic comparison of different lattice Boltzmann models for thermal and flow field in the phase-change process is numerically conducted in a square cavity; the numerical results are validated by the literature data. The computational results show how the transient phase-change process, expressed in terms of the volume melt fraction of phase change materials, depends on the thermal and geometrical parameters of the system.
A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.
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