A fast breeder reactor (FBR) is considered as the promising technology in terms of load reduction on the environment, because the FBR has capability to improve usage efficiency of uranium resources and can reduce high-level radioactive waste which needs to be managed for millions of years. A cold trap is one of the important components in the FBR to control the impurity concentration of the liquid sodium. For accurate evaluation of the cold trap performance, we have been proposing the three-dimensional (3D) numerical analysis method of the cold trap. In this method, the evaluation of the impurity precipitation phenomena on the surface of the mesh wire of the cold trap is the key. For this, the numerical analysis method which is based on the lattice kinetic scheme (LKS) has been proposed. In order to apply the LKS to the impurity precipitation simulation of the cold trap, two models (the low Reynolds number model and the impurity precipitation model) have been developed. In this paper, we focused on the validation of these models. To confirm the validity of the low Reynolds number model, the Chapman–Enskog analysis was applied to the low Reynolds number model. As a result, it has been theoretically confirmed that the low Reynolds number model can recover the correct macroscopic equations (incompressible Navier–Stokes equations) with small error. The low Reynolds number model was also validated by the numerical simulation of two-dimensional (2D) channel flow problem with the low Reynolds number conditions which correspond to the actual cold trap conditions. These results have confirmed that the error of the low Reynolds number model is ten times smaller than that of the original LKS. The validity of the impurity precipitation model was investigated by the comparison to the precipitation experiments. In this comparison, the mesh convergence study was also conducted. These results have confirmed that the proposed impurity precipitation model can simulate the impurity precipitation phenomena on the surface of the mesh wire. It has been also confirmed that the proposed impurity precipitation model can simulate the impurity precipitation phenomenon regardless of the cell size which were tested in this investigation.