Comparison of coupling techniques in a high-order discontinuous Galerkin-based particle-in-cell solver

Highly rarefied plasma flows in technical devices are physically modelled by the Maxwell?Lorentz equations. They combine the solution of the Maxwell equations, where the electric field E and magnetic induction B are determined, with the Lorentz system, accounting for the movement of charged particles due to the electromagnetic forces. To solve these equations for complex-shaped domains, a fully electromagnetic particle-in-cell (PIC) code has been developed using high-order discontinuous Galerkin methods for the Maxwell equations on a computational mesh, coupled with a Lorentz solver on the basis of a second-order leapfrog scheme, acting on the particles at their current positions. Since the particles move freely in space, the mesh-based and the mesh-free values have to be coupled. This coupling includes the deposition of the charge and current densities from the current particle positions onto the mesh as well as the interpolation of the electromagnetic fields from the mesh to the actual particle positions. Both steps have to be computed with appropriate accuracy. Different approaches to particle-grid coupling within the PIC solver have been investigated. In this paper, these concepts are described and corresponding simulation results with respect to accuracy and computational demand are presented.

[1]  R. Fonseca,et al.  Three-dimensional Weibel instability in astrophysical scenarios , 2003 .

[2]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[3]  E. S. Weibel,et al.  Spontaneously Growing Transverse Waves in a Plasma Due to an Anisotropic Velocity Distribution , 1959 .

[4]  Chi-Wang Shu,et al.  Discontinuous Galerkin Methods: Theory, Computation and Applications , 2011 .

[5]  Pascal Omnes,et al.  A finite volume method for the approximation of Maxwell's equations in two space dimensions on arbitrary meshes , 2008, J. Comput. Phys..

[6]  Pierre Degond,et al.  On a finite-element method for solving the three-dimensional Maxwell equations , 1993 .

[7]  D. Hammer,et al.  Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas , 1972 .

[8]  Jerold W. Emhoff,et al.  Grid-free plasma Simulation techniques , 2006, IEEE Transactions on Plasma Science.

[9]  O. Buneman,et al.  Time-Reversible Difference Procedures , 1967 .

[10]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[11]  J. Bittencourt.  Transport Processes in Plasmas , 2004 .

[12]  Jan S. Hesthaven,et al.  Simulations of the Weibel instability with a High-Order Discontinuous Galerkin Particle-In-Cell Solver , 2006 .

[13]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[14]  Claus-Dieter Munz,et al.  Hybrid Code Development for the Numerical Simulation of Instationary Magnetoplasmadynamic Thrusters , 2008, High Performance Computing in Science and Engineering.

[15]  J. Verboncoeur.  Particle simulation of plasmas: review and advances , 2005 .

[16]  Claus-Dieter Munz,et al.  Polymorphic nodal elements and their application in discontinuous Galerkin methods , 2009, J. Comput. Phys..

[17]  M. Turner.  Kinetic properties of particle-in-cell simulations compromised by {M}onte {C}arlo collisions , 2006 .

[18]  R. Morse,et al.  NUMERICAL SIMULATION OF THE WEIBEL INSTABILITY IN ONE AND TWO DIMENSIONS. , 1971 .

[19]  Arne Taube,et al.  A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations , 2009 .

[20]  Claus-Dieter Munz,et al.  Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model , 2000 .

[21]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[22]  D. Quemada,et al.  Anisotropic Temperature Plasma Instabilities , 1968 .

[23]  Jan S. Hesthaven,et al.  High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids , 2006, J. Comput. Phys..

[24]  Claus-Dieter Munz,et al.  A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes , 2000 .

[25]  J. Hesthaven,et al.  Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , 2007 .

[26]  R. Lewis,et al.  Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations , 2000 .

[27]  Claus-Dieter Munz,et al.  A finite-volume particle-in-cell method for the numerical treatment of Maxwell-Lorentz equations on boundary-fitted meshes , 1999 .

[28]  Charles K. Birdsall,et al.  Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC , 1991 .

[29]  John W. Luginsland,et al.  On the elimination of numerical Cerenkov radiation in PIC simulations , 2004 .