Institute of Aerodynamics and Gas Dynamics
- Discontinuous Galerkin (DG)
- Particle-In-Cell (PIC)
- Maxwell’s equations
- Implicit time integration
- Particle-Mesh Coupling
- High Performance Computing (HPC)
In PIC schemes, several time step restrictions are encountered. The Maxwell solver is limited by the CFL condition arising from an explicit time integration. Additionally, the particle oscillation has to be resolved. For a cold plasma, the explicit time step of the particles can be several hundreds or thousands of times the time step of the Maxwell solver. Semi-implicit PIC solver treat the Maxwell’s equations implicitly and the particles remain explicit. These schemes offer the advantage of similar time steps for both parts of the PIC solver. Research for the efficient implicit time integration of high-order schemes is still ongoing. Especially, the implicit treatment of purely hyperbolic equation remains a challenge.
In PIC schemes, the particles are treated in a Lagrangian manner and the Maxwell solver is grid based. Efficiency gains of the particle-mesh coupling promises large reductions of computational time. Furthermore, high-order methods required curved meshes. A combined scheme requires the capability of particle tracking algorithms to handle curvilinear meshes. For high-order schemes, the particle-mesh coupling offers a wide opportunity for optimization.
Three-dimensional High-Order Semi-Implicit Particle-in-Cell Solver based on Discontinuous Galerkin Spectral Element Method Presentation
Curvilinear Particle-in-Cell Code on Arbitrary, Unstructured Grids Presentation
Nagel, W E; Kröner, D H; Resch, M M (Ed.): High Performance Computing in Science and Engineering ‘14, Springer, 2015, ISBN: 978-3-319-10810-0.
Comptes Rendus Mécanique, 342 (10-11), pp. 662–670, 2014, ISSN: 1631-0721.