Space-time DG-FEMs for Fluid and Kinetic Plasma Models

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

The investigator, along with his students and collaborators, will develop efficient high-order time-stepping methods that will be used in conjunction with discontinuous Galerkin spatial discretizations. In particular, adaptive space-time methods will be developed that will allow for either (1) explicit local time-stepping that allows for different time-steps in different flow regimes, or, (2) implicit time-stepping, which is sometimes required in certain applications. A key feature that will be integrated into these numerical schemes is error control in the form of adaptive mesh refinement. Several error estimators will be investigated, as well as several shock-capturing strategies. The resulting numerical schemes will be applied to a variety of model equations that arise in plasma physics, including ideal magnetohydrodynamics, two-fluid Euler-Maxwell, and kinetic Vlasov equations. Specific application problems that are of interest include the dynamics of solar coronal loops, the formation and propagation of astrophysical jets, and the simulation of collisionless magnetic reconnection. Plasma is the fourth state of matter (after solid, liquid, and gas), which can be characterized as an ionized gas (i.e., a gas that is able to conduct electricity). Plasma appears in a wide range of applications including astrophysics and space physics, as well as in laboratory settings such as in magnetically confined fusion. Modeling and understanding the basic phenomenon in plasma have long been topics in scientific computing, yet many problems remain far too numerically intensive for modern parallel computers. The main difficulty is that plasmas span a wide range of spatial and temporal scales. The scope of this research is to develop accurate and efficient computational methods that can better solve various equations that model plasma behavior. A key aspect of this research is the development of adaptive numerical methods that are able to dynamically estimate and control the errors that are produced during the course of a computation.