Lattice Boltzmann Method (LBM) and Alternating Direction Implicit Method (ADI) in Solving 2-D Transient Heat Conduction Problems

Different numerical methods are commonly used to solve transient heat conduction problems. This investigation centers on the simultaneous utilization of the lattice Boltzmann method (LBM) and the Alternating direction implicit method (ADI) for solving two-dimensional conduction heat transfer problems within a metal plate. Problems in two-dimensional rectangular geometries have been considered. In the 2D geometry, the east and west boundaries are thermally insulated, while the other boundaries have prescribed temperatures. The main objective of this study is to demonstrate that the Lattice Boltzmann Method (LBM) and the Alternating Direction Implicit (ADI) method are capable of solving the heat transfer equation, particularly by employing an energy equation for solid phases. Additionally, the study aims to analyze the effects of thermal boundary conditions, with a particular emphasis on their automatic impact at the interface.