A hybrid regularized lattice Boltzmann model for convection-diffusion equation

In this work, a lattice-Boltzmann model for advection-diffusion equation is presented, built upon the regularized model. In the regularized collision model of this paper, the coefficients in the reconstruction process of the offequilibrium distribution are evaluated through two different methods. The first method arises from direct projection of off-equilibrium distribution, while the second method is computed as to best approximate the scalar diffusion flux. By combining the two methods and introducing proportional coefficients, a hybrid regularized collision model is obtained. In terms of model validations, test cases of smooth problems and discontinuous problems are selected. The results are compared with those obtained by the Bhatnagar-Gross-Krook model and the projection reconstruction model. First, the calculation accuracy of the model in solving the smooth distribution problem is verified by the periodic one-dimensional problem and the advection-diffusion process of the two-dimensional Gaussian distribution. Then, the cases of discontinuous problems are considered for the demonstration of the numerical stability of the model. The results show that the hybrid regularization lattice Boltzmann model retains the advantages of the regularization model in terms of calculation accuracy, and at the same time has good numerical stability in solving discontinuous problems.