(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, the stability of the regularized lattice Boltzmann method (RLBM) for convection-diffusion equations is studied. First, it is shown that the evolution equation of RLBM can be transformed into two macroscopic difference schemes, one is explicit and the other is implicit. Compared with the traditional mesoscopic evolution equation, the macro evolution equation has simpler form, lower order of growth matrix, higher computational efficiency and less memory. Then, for the linear convection-diffusion equations without the source term, we use Fourier analysis to prove that the three schemes have exactly the same stability region. For the one-dimensional diffusion equation, we have proved the theoretical stability. For the D1Q3 model, D2Q5 model and D2Q9 model, we have studied the numerical stability. Our results have also been compared with related work by others, which shows they match well. Finally, we conducted some numerical tests to verify that our stability results are credible.