The random walking method for the steady linear convectiondiffusion equation with axisymmetric disc boundary

In this article, the random walking method is used to solve the steady linear convection-diffusion equation (CDE) with disc boundary condition. The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained. The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method. The proposed method is tested through two numerical cases. The results show that the random walking method can solve the steady linear CDE effectively. The influence of the parameters on the results is also studied. It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.