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In this paper, a new two-relaxation-time regularized (TRT-R) latticeBoltzmann (LB) model for convection-diffusion equation (CDE) with variablecoefficients is proposed. Within this framework, we first derive a TRT-Rcollision operator by constructing a new regularized procedure through thehigh-order Hermite expansion of non-equilibrium. Then a first-orderdiscrete-velocity form of discrete source term is introduced to improve theaccuracy of the source term. Finally and most importantly, a new first-orderspace-derivative auxiliary term is proposed to recover the correct CDE withvariable coefficients. To evaluate this model, we simulate a classic benchmarkproblem of the rotating Gaussian pulse. The results show that our model hasbetter accuracy, stability and convergence than other popular LB models,especially in the case of a large time step.

Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with variable coefficients