Abstract
The lattice Boltzmann method (LBM) has attracted much attention in recent years as a recent efficient solution method for fluid flow simulations as well as general PDEs. Due to the local nature of the computations in the lattice Boltzmann method and its ease of programming, the LBM is an ideal candidate for developing efficient parallel PDE solvers suitable for recent computer hardware. In the present study, we have used the lattice Boltzmann method for solving the transient heat diffusion equation. The performance of this method is compared with that of the traditional finite difference based PDE solver. All these solvers have been developed using the Julia programming language, which is a recent player amongst the scientific computing languages. Several benchmark problems in the field of transient heat transfer described by parabolic PDEs are solved, and the results obtained from the aforementioned methods are compared with each other. It is shown that by using the lattice Boltzmann method, it is possible to solve these partial differential equations more efficiently while maintaining the accuracy of the solution.
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