Study On Gas Discharge Equations By Lattice Boltzmann Method And Its Applications Of Streamer Simulations

Currently,numerical simulation is becoming a significant method for promoting the development of gas discharge theory.By comparing simulation results and experimental results,and continuously improving the numerical calculation methods,the more actual model is set up.The research of numerical simulation increases understanding on gas gap discharge process and promotes the development of the theory of gas discharge.In recent years,streamer discharge is turning into an important part of simulation study of gas discharge and starting point.Moreover,it is the key problem to solve a system of partial differential equations composed by particle transport equations and Poisson equation.In allusion to the problem,this thesis innovatively applied the lattice Boltzmann method to solve the equations system.In recent years,the lattice Boltzmann method is applied to solve some partial differential equations.Lattice Boltzmann method,which utilizes micro model to simulate the macro transport phenomena,has been successively applied in multiple field.In this thesis,the problems of non-physical oscillation,non-structure grid difference and non-satisfied local conservation law are introduced to solve the system of partial differential equations.Indeed,the lattice Boltzmann method can not only solve the problems,but also greatly simplify the difficulty and complexity of calculation and program design.In the meanwhile,this method can solve parabolic partial differential equations and elliptic partial differential equations in one model.All in all,it has its unique advantages.This thesis focuses on the application of lattice Boltzmann in nanosecond scale and two-dimensional streamer discharge.Additionally,this thesis adopts the original fluid kinematics model to simulate streamer discharge by selecting scales with different parameters.In the mixed-dimensional models,one-dimensional particle transport equations are calculated using the lattice D1Q3 model.The significant parameter ? is solved by multi scale expansion,Taylor expansion and restoration of the original equation.Furthermore,two-dimensional streamer discharge model,and the particle transport equations are calculated by utilizing the D2Q9 velocity discretization scheme and lattice frame extrapolation boundary scheme,solving twodimensional Poisson equation with finite difference,and designing coupling algorithm of transport equation and Poisson equation.After that,a simulation program was coded.The discharge process of mixed dimensional cathode streamer and double streamer are simulated,and meanwhile,the charge density draw and electric field draw are displayed.Moreover,the two-dimensional electric field distribution in discharge domain and particle density variation is studied by twodimensional simulations.The model is verified by comparing simulation results to references.Beyond that,this thesis utilizes the numerical simulation model to analyze the impact of ionization coefficient as well as electron transfer rate in the process of streamer discharge.This thesis shows the advantages of utilizing the lattice Boltzmann simulation of streamer discharge as well as its application prospect.Compared with traditional partial differential equations model,the lattice Boltzmann method is much easier in mathematical physics model,simpler in computer program design,as well as more accurate and more suitable for parallel computing.This thesis discusses the feasibility of applying Boltzmann method on GPU to achieve large parallel computation,and verify the efficiency of GPU.Finally,this thesis shows the prospects of applying lattice Boltzmann method into electronic engineering for the future.