Discrete Unified Gas Kinetic Scheme For Plasma Flows And Its Applications

As the fourth state of matter,plasma occupies 99% of the total matter in the universe,which is widely used in the space and astrophysics,magnetic confinement fusion,space electric propulsion and material processing and so on.As a bridge between theory and experiment,computational plasma is an important tool for understanding complex plasma behavior.Due to the extensive physical parameters of plasma,its characteristic space and time scale spans multiple orders of magnitude.This multiscale feature has brought great challenges to the development of high-fidelity and efficient methods.Kinetic simulation is an effective way to develop high-fidelity methods.Recently,the discrete unified gas kinetic scheme(DUGKS)has been proposed,which can effectively simulate the multiscale flows.However,current DUGKS is mainly investigated in neutral gas,and has not been applied for plasma simulation.As a result,the main purpose of this thesis is to develop a high-fidelity and economic DUGKS for multiscale plasma simulation.The main research contents of this thesis are as follows:First,the conservative DUGKS is developed to solve the kinetic equations,while a general finite element method is developed to solve electromagnetic field equations.These two solvers are the basis of plasma kinetic simulation,which are independently verified by several numerical experiments.Numerical results show that,due to the coupling of particle collision and transport,conservative DUGKS can be used to simulate the flow in all collisional regimes as well as preserves better conservation property.Second,based on the conservative DUGKS and general finite element method,electrostatic DUGKS is proposed for collisional plasma characterized by Knudsen number Kn,where the numerical parameters(spatial and temporal mesh sizes)are not limited by Kn.This is the first expansion of DUGKS in plasma simulations.Besides,a comparative study of current DUGKS with a general particle in cell(PIC)method is also presented.Numerical results demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes,while the PIC method is desired for the field-dominated plasma flows involving a wide range of velocities.Third,based on electrostatic DUGKS and reformulated Poisson equation,the evolution of distribution function and field equation are coupled in an appropriate way.Then a multiscale electrostatic DUGKS is developed for plasma in all electrostatic regimes characterized by Kn and normalized Debye length λ.The current method removes the restriction of characteristic parameters Kn and λ on numerical ones,and has a comparable numerical cost per time step to that of traditional kinetic methods.Numerical experiments show that proposed DUGKS can provide high-fidelity and economic solutions in all electrostatic plasma regimes.Furthermore,based on multiscale electrostatic DUGKS and reformulated Maxwell equations,a simple and efficient way is proposed to couple microscopic particles and field equations.Then a multiscale electromagnetic DUGKS is developed for plasma in all electromagnetic plasma regimes characterized by Kn,λ and normalized Larmor radius r.With different characteristic parameters,current DUGKS automatically adapts to the consistent solution of MHD or the Vlasov-Maxwell system,where numerical parameters are not limited by Kn,λ and r.Several numerical experiments are presented to validate the multiscale electromagnetic DUGKS.Finally,combined with current accelerated computing technology,the applications of DUGKS in plasma engineering and scientific research are investigated.The multiscale electrostatic DUGKS combined with adaptive grid in velocity space is used to study the influence of inject density and screen grid voltage on the performance of ion optical system.The use of adaptive grid improves the efficiency of DUGKS by an order of magnitude,which can be comparable to PIC.The results suggest that the ion density and screen grid voltage should be appropriately determined to ensure that system operates under normal focused condition.In addition,multiscale electromagnetic DUGKS combined with the mass ratio scaling technology is used to study the influence of guide magnetic field and plasma collision on magnetic reconnection.The results show that the guide field breaks the symmetrical structure,while the collision makes the flow tend to be isotropic.The larger the guide field or the stronger the collision is,the slower the magnetic reconnection becomes.Encouragingly,DUGKS firstly reproduces collisionless and strong collision magnetic reconnection.In summary,this thesis firstly extends DUGKS to plasma simulation,and systematically develops DUGKS for multiscale electrostatic and electromagnetic plasma,as well as explore its feasibility in practical engineering and scientific research.The research work in this thesis provides a novel research way for understanding complex plasma behavior.