In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to...In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to convert the nD CDE into a diffusion equation.Then,the converted diffusion equation is solved by the LB model.So,compared to the available LB models for CDE,the present LB model can eliminate the difficulty in treating the convection term.With the direct Taylor expansion method,it is shown that the CDE can be exactly derived from the exponential transformation based LB model.Finally,a variety of numerical tests have been conducted to validate the present LB model.It can be found that the numerical results agree well with the analytical solutions.Moreover,we also find that the present LB model has second-order convergence rate in space,and it is more effective and more stable than the previous LB model for the CDE.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant Nos.12072127 and 11702259)the Guidance Project of Scientific Research Program of Hubei Provincial Department of Education(Grant No.B2021322).
文摘In this paper,an exponential transformation based lattice Boltzmann(LB)model for solving the n-dimensional(nD)convection-diffusion equation(CDE)is developed.Firstly,a class of exponential transformation is proposed to convert the nD CDE into a diffusion equation.Then,the converted diffusion equation is solved by the LB model.So,compared to the available LB models for CDE,the present LB model can eliminate the difficulty in treating the convection term.With the direct Taylor expansion method,it is shown that the CDE can be exactly derived from the exponential transformation based LB model.Finally,a variety of numerical tests have been conducted to validate the present LB model.It can be found that the numerical results agree well with the analytical solutions.Moreover,we also find that the present LB model has second-order convergence rate in space,and it is more effective and more stable than the previous LB model for the CDE.
