Stability of Regularized Lattice Boltzmann Model for Convection-Diffusion Equations (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 mesoscopicevolution equation, the macro evolution equation has simpler form, lower order ofgrowth matrix, higher computational efficiency and less memory. Then, for the linear convection-diffusion equations without the source term, we use Fourier analysisto 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 D1Q3model, D2Q5 model and D2Q9 model, we have studied the numerical stability. Ourresults have also been compared with related work by others, which shows they matchwell. Finally, we conducted some numerical tests to verify that our stability results arecredible.