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978-3-8439-4236-2, Reihe Ingenieurwissenschaften

Philip Ortwein Implicit Time Integration Strategies for a Particle-in-Cell Solver

188 Seiten, Dissertation Universität Stuttgart (2019), Softcover, A5

A variety of physical problems deal with dilute plasma flows, such as space weather forecast or spacecraft propulsion. An understanding of underlying physical phenomena can be obtained by the aid of numerical simulations. The standard method used for such simulations is the particle-in-cell method, which combines an Eulerian electromagnetic field solver and a Lagrangian particle solver in a self-consistent approach.

An efficient explicit time integration requires particle moving close to the speed of light. If the particles move with a velocity much slower than the speed of light, like in plasma thrusters, a scale difference between the stability condition of the field solver and the accuracy constraint of the particle pusher arises. This problem is exacerbated by the mass ratio between ions and electrons. In order to resolve the kinetics of ions, several thousand time steps of the field solver and electrons are necessary. Therefore, simulations of many problems are not feasible due to the large computational cost. In this thesis, the limitation of the explicit time integration is overcome by presenting a novel implicit Runge-Kutta solver based on Runge-Kutta methods. This requires the implicit treatment of the field and particle solvers.

In this work, it is demonstrated that implicit methods exceed the efficiency of an explicit particle-in-cell solver. The implicit-explicit Runge-Kutta approach is especially convincing and it offers a high flexibility by splitting the particle terms into explicit and implicit terms. This allows adapting to the encountered plasma conditions and maximizes the computational efficiency. The derived implicit methods result in a computational gain of up to three-orders of magnitude.