P. Ortwein

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.

Complex-Frequency Shifted PMLs for Maxwell’s Equations With Hyperbolic Divergence Cleaning and Their Application in Particle-in-Cell Codes

The simulation of unbounded domains inevitably requires an artificial truncation of the computational domain and spurious reflections resulting from this procedure are a common problem. In this paper, a perfectly matched layer formulation for Maxwells equations in purely hyperbolic form is presented. The model is applied to standard wave attenuation problems and particle-in-cell simulations of electron beam devices.

Coupled PIC-DSMC Simulations of a Laser-Driven Plasma Expansion

In the field of material processing or spacecraft propulsion, laser ablation is used to remove material from a solid surface with a laser beam. The numerical study of this process has been directed towards direct laser-solid interactions, tackled by molecular dynamics simulations which have been conducted in the past. An additional field of interest arises, when considering the interaction of a laser beam and the plasma created by former laser impacts. For this purpose, an Message Passing Interface parallelized, high-order Particle-in-Cell scheme coupled with a Direct Simulation Monte Carlo method is used to handle the complex phenomena, which usually are simulated using disjoint techniques. The complete scheme is constructed to run on three-dimensional unstructured hexahedra, where for the Particle-in-Cell solver, a highly efficient discontinuous Galerkin method is used to calculate the electromagnetic field. Simulations under realistic settings require the use of high performance computing, where the parallel performance of the coupled solver plays the most important role. This work offers insight into such an undertaking by simulating the expansion of a plasma plume in three dimensions using this coupled algorithm.

Recent developments of DSMC within the reactive plasma flow solver PICLas

In order to enable the numerical simulation of rarefied plasma flows in thermal and chemical non-equilibrium, electro-magnetic interactions as well as particle collisions have to be considered. A common approach is to use particle-based methods. The Particle-in-Cell (PIC) method simulates charged collisionless gas flows by solving the Vlasov-Maxwell equation system while particle collisions in neutral reactive flows are treated by the Direct Simulation Monte Carlo (DSMC) method. Therefore, PICLas is being developed, a coupled simulation code that enables three-dimensional particle-based simulations combining high-order PIC and DSMC schemes for the simulation of reactive, rarefied plasma flows. PICLas enables time-accurate simulations on unstructured hexahedral meshes and is parallelized for high-performance computing. In addition to an overview of PICLas, the current development status of the DSMC module is presented. This includes the relaxation of polyatomic gases, the extension of the chemical modeling...

A particle localization algorithm on unstructured curvilinear polynomial meshes

Abstract Many particle-based methods require a coupling between particle motion and fluid flows or fields. The particle motion is approximated in phase space, while the fluid flows or fields are calculated on a fixed Eulerian frame of reference. In this work, we present algorithms for locating and tracing particles through curvilinear and unstructured hexahedral meshes. Special attention is given to accurately compute the intersections of particles with polynomial curvilinear faces. We derive two localization algorithms, which locate particles either by tracing in physical space or restricting the tracing step to boundary faces and determining the particles position in reference space. The proposed algorithms are validated by three-dimensional charged particle simulations in electromagnetic fields.

Implicit time integration for particle treatment within a Particle-in-Cell solver

Summary form only given. Previously, a semi-implicit Particle-in-Cell (PIC) solver based on a high-order Discontinuous Galerkin Spectral Element Method has been developed. In this scheme, particles are treated explicitly, while Maxwells equations are solved implicitly with a matrix-free Krylov subspace method. This allows surpassing the CFL condition of the Maxwell solver that couples the time step to the light velocity. Another severe time step restriction due to stability in an explicit time approximation may occur due to fast moving particles. If the time evolution of these fast particles influences the solution only weakly, then this limitation may also be mitigated by treating the particle motion with an implicit time integration method.Approximating the equation of motion implicitly requires solving a non-linear system for each particle. Here, a Jacobian-free Newton-Krylov approach is chosen, freeing the scheme from the requirement to construct the Jacobian matrix1. The time integration is performed by a third or fourth order Runge-Kutta scheme2. In the conference presentation, the author introduces the new numerical scheme and compares it to the existing explicit and semi-explicit PIC solver.

Three-dimensional, high-order semi-implicit particle-in-cell solver based on a Discontinuous Galerkin Spectral Element Method

Summary form only given. A fully three-dimensional, explicit high-order Discontinuous Galerkin Spectral Element Method (DGSEM) based Particle-In-Cell (PIC) solver, targeted for the simulation of high power microwave devices, is adapted for simulations of ionized plasmas. A strong limitation of the explicit time integration is the stability restriction of the Maxwell solver by the CFL condition. This leads to unfavorable long simulation times for ionized, slow evolving plasmas. Semi-implicit time integration overcomes these limitations by treating the Maxwell solver implicitly. A fourth-order implicit-explicit Runge-Kutta scheme is the method of choice. The solving strategy of the linear solver in each Runge-Kutta step is important. Inverting and storing the system matrix is impossible for a parallel, three-dimensional solver due to the large storage requirements. Iterative solvers like a matrix-free Krylov subspace method have to be applied. A preconditioner is mandatory to increase the convergence rate, while its application should preserve the scalability of the DGSEM scheme. In the conference presentation, the authors show the numerical methods and their implementation. The semi-implicit scheme is validated against the explicit solver, showing the limits and benefits of a semi-implicit PIC solver.