Performance of thermal lattice Boltzmann and finite volume methods for the solution of heat conduction equation in 2D and 3D composite media with inclined and curved interfaces

In the present study, the accuracy of predicted effective thermal conductivity of composite materials, determined by the finite volume method (FVM) and the thermal lattice Boltzmann method (TLBM) using single relaxation time (SRT), is investigated. In addition, computational efforts required by both solution methods are also compared. Two- and three-dimensional heat conduction problems in two-phase domains with a high thermal conductivity ratio are considered, where oblique and curved interfaces are represented by the staircase approximation. The discretisation is carried out on a uniform mesh. For TLBM, different stencils are employed and a wide range of relaxation frequencies, corresponding to relative magnitudes of thermal conductivities of different phases, is investigated. For comparison, wherever available, the analytical expression for the effective thermal conductivity is considered. Otherwise, the reference effective thermal conductivity is determined using a commercial software employing an appropriate body-fitted mesh. The present results show that the accuracy of TLBM depends on the employed stencil, relaxation frequency and arrangement of two materials in the computational domain. It is also observed that TLBM can be even more accurate than FVM, although the accuracy of FVM is independent of individual values of thermal conductivities. For the same convergence criterion, however, TLBM requires a higher number of iterations than FVM, although TLBM shows a potential for speed-up.