Micro-Macro Decomposition Numerical Schemes for Multiscale Simulation of Plasma

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Plasma physics is the study of the dynamics of ionized gases. Because plasma, often referred to as the fourth state of matter, is the most abundant form of ordinary matter in the universe, there exist many important application problems for which an understanding of the plasma dynamics is critical. Some examples of these applications include understanding the dynamics of stars, the affect of the solar wind on the Earth's magnetosphere, the dynamics of magnetically confined fusion devices, and the dynamics of laser-plasma devices that could be used in medical imaging applications. The objective of this research is to develop highly accurate and efficient computational tools for simulating the dynamics of the electrons (negatively charged particles) and the ions (positively charged particles) that constitute the plasma of interest. This research aims to develop novel computational techniques based on novel multiscale methods that divide the underlying equations into macroscopic (large scale phenomena) and microscopic (small scale phenomena), and couple these scales in some appropriate manner. These methods will be implemented in computer code that will take advantage of modern parallel computer architectures. The resulting methods and codes will be used to simulate various application problems in order to verify and validate the approach.The primary objective of this research is to develop accurate and efficient computational methods for solving nonlinear differential equations used to model plasma dynamics. The goal is to solve a class of multiscale models of plasma using a novel micro-macro decomposition approach. The idea behind the micro-macro decomposition is to start with a general enough model that contains the coupled dynamics of macroscopic and microscopic phenomena, to then write this model into two parts with appropriate coupling terms, and finally to apply potentially different numerical techniques to each part in order to optimize efficiency. The specific schemes that will be used in this research are based on high-order discontinuous Galerkin finite element methods with novel time-stepping strategies to achieve computational efficiency. This research will develop new computational tools for simulating plasma dynamics. In particular, new micro-macro decomposition techniques will be designed and implemented that allow for the efficient numerical solution of multi-species plasma systems. New strategies will be developed to adaptively turn on and off the microscopic solvers. As part of the research project, novel computational methods and software will be produced that in the future could be applied to a wide range of both laboratory and astrophysical plasma problems. The software developed will be made freely available on the web as part of the DoGPack software project.