Optimization And Applications Of Lattice Boltzmann Method For Electro-Convection And Electro-Thermo-Convection

Interactions between charged particles（such as ions）and electric field,flow field,as well as temperature field are the primary cause of the electro-and thermo-convection（EC and ETC）.This kind of flow contains rich and profound physical connotations.However,relevant analysis and research have been relatively scarce in the field due to the complexity of the mathematical problem and huge computational consumption.In response to this situation,we provided an optimization scheme that can be used in EC and ETC flows based on a two-relaxation time lattice Boltzmann method（TRT-LBM）.Furthermore,a high-performance parallel program was built based on CUDA to modeling the three-dimensional ETC flows.Through numerical simulations,a comparison study has been performed to test the scheme,and analysis of flow and heat transfer characteristics of three-dimensional ETC is also introduced.According to the features of LBM,the linear discrete velocity model（LDVM）with simpler and more intuitive form can replace the full discrete velocity model（FDVM）in modeling convection-diffusion equation（CDE）.To verify this point,we derived analytically the LDVM,i.e.,D2Q5 and D3Q7 and FDVM,i.e.,D2Q9 and D3Q27,for the ion transport equation（convection-diffusion-drift equation）in both two-and three-dimensional systems in EC.Numerical accuracy,stability,and efficiency are compared between these two models.Through the Chapman-Enskog analysis,it was found out that there exist extra error terms in the LDVM compared with FDVM,which is of higher orders and can be neglected in practical simulations.In addition,the results of theoretical analysis are verified by numerical simulation and the two model’s error terms are calculated and outputted.With the EC flows between two parallel plate electrodes,for example,the numerical results of LDVM and FDVM are quantitatively compared in both two-and three-dimensional systems.It is found that the LDVM can substitute FDVM in certain conditions with a substantial saving in computational costs and a small sacrifice in accuracy.Finally,the LDVM is applied to three-dimensional ETC system,typical structures such as the rolling pattern and cell pattern（including square pattern and hexagonal pattern）are obtained.It is found that the ETC flow contains typical characteristics of both EC and Rayleigh-Bernard convection（RBC）.On this basis,the cell pattern of ETC flow was analyzed emphatically,both flow and heat transfer mechanisms under the action of electric field were explored.For the square pattern,we analyzed two stable structures of the flow and investigated the influence of parameters.Furthermore,the coupling mechanism of Coulomb force and buoyancy forces is deeply explored in this case.For the hexagonal pattern,we analyzed its structure and heat transfer mechanism for the steady flow,computed the distribution of Nusselt number（Nu）at the hot wall,and investigated the variation of the average Nusselt number(Nu_ave)with driving parameters T.Results show that the curve roughly satisfies the quadratic function relation.