T. Stindl

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.

Hybrid Code Development for the Numerical Simulation of Instationary Magnetoplasmadynamic Thrusters

This paper describes the numerical modeling of rarefied plasma flows under conditions where continuum assumptions fail. We numerically solve the Boltzmann equation for rarefied, non-continuum plasma flows, making use of well known approaches as PIC (Particle in Cell) and as DSMC (Direct Simulation Monte Carlo). The mathematical and numerical modeling is explained in some detail and the required computational resources are investigated.

Parallel Performance of a Discontinuous Galerkin Spectral Element Method Based PIC-DSMC Solver

Particle based methods are required to simulate rarefied, reactive plasma flows. A combined Particle-in-Cell Direct Simulation Monte Carlo method is used here, allowing the modelling of electromagnetic interactions and collision processes. The electromagnetic field solver of the Particle-in-Cell method has been improved by switching to a discontinuous Galerkin spectral element method. The method offers a high parallelization efficiency, which is demonstrated in this paper. In addition, the parallel performances of the complete Particle-in-Cell module and the Direct Simulation Monte Carlo module are presented.

Development of a Two Phase Solver Accounting for Solid Particles in Continuum Gas Flows

The Euler-Lagrangian approach is used for the simulation of solid particles in hypersonic entry flows. For flow field simulation, the program SINA (Sequential Iterative Nonequilibrium Algorithm) developed at the Institut fur Raumfahrtsysteme is used. The model for the effect of the carrier gas on a particle includes drag force only. Other parameters like lift Magnus force or damping torque are not taken into account so far. The reverse effect of the particle phase on the gaseous phase is currently neglected. Parametric analysis is done regarding the impact of variation in the physical input conditions like position, velocity, size and material of the particle. Convective heat fluxes onto the surface of the particle and its radiative cooling are discussed. The variation of particle temperature under different conditions is presented. The influence of various input conditions on the trajectory is explained. A semi empirical model for the particle wall interaction is also discussed and the influence of the wall on the particle trajectory with different particle conditions is presented.

Three-Dimensional Gyrotron Simulation Using a High-Order Particle-in-Cell Method

A three-dimensional highly parallelized code for plasma simulation based on the Particle-In-Cell (PIC) approach using a discontinuous Galerkin method has been developed and validated within the instationary magneto-plasma dynamic (IMPD) thruster project (Associated with the DFG project “Numerical Modeling and Simulation of Highly Rarefied Plasma Flows”). With this code, it is for the first time possible to simulate the highly challenging gyrotron launcher and resonator, i.e. a high-energetic microwave source used for fusion-plasma heating, without using any physical approximations. We present the results of the gyrotron simulations with special focus on the parallelization capabilities of our code. For the gyrotron launcher, computations with up to 2048 processes have been performed. Parallel scaling of the PIC code with at most 1024 processes for simulating the gyrotron resonator is investigated in detail.

Efficient Parallelization of a Three-Dimensional High-Order Particle-in-Cell Method Applied to Gyrotron Resonator Simulations

Growing computational capabilities and simulation tools based on high-order methods allow the simulation of complex shaped plasma devices including the entire nonlinear dynamics of the Maxwell-Vlasov system. Such simulations model the particle-field-interactions of a non-neutral plasma without significant simplifications. Thereby, new insights into physics on a level of detail that has never been available before provide new design implications and a better understanding of the overall physics. We present a high-order discontinuous Galerkin method based Particle-In-Cell code for unstructured grids in a parallelization framework allowing for large scale applications on HPC clusters. We simulate the geometrically complex resonant cavity of the 170 GHz gyrotron aimed for plasma resonance heating of the fusion reactor ITER and we demonstrate that a highly efficient parallelization is a crucial requirement to simulate such a complex large-scale device.

Three-dimensional simulation of rarefied plasma flows using a high order particle in cell method.

A three-dimensional Particle In Cell scheme for unstructured grids is presented. Since simulations of this kind require large computational resources, the solver was parallelized. The scalability of two parallel simulations is shown and an engineering application as well as two validation test cases for the scheme are presented.