Dual Comprehensive Exam of CMSE Carolyn Wendeln

Department of Computational Mathematics, Science & Engineering and Department of Physics & Astronomy

Abstract:
Plasma, the fourth state of matter, makes up 99% of the baryonic matter in our universe. From our ionosphere, to stars, galaxy clusters, and beyond, plasmas are found everywhere. A common feature often associated with plasma is turbulence. Turbulence is characterized by the complex, chaotic motion of a fluid. This convoluted motion becomes exacerbated when the fluid is electrically conducting. One way to study turbulence in plasmas is through the magnetohydrodynamic (MHD) equations of motion. In this comprehensive we will go over the history and numerical techniques used to study MHD turbulence, and we will discuss the current numerical limitations faced. We will then introduce a high order, weighted essentially non oscillatory scheme for hyperbolic conservation laws (WENO-HCL) as a way to model MHD turbulence. We will then show several numerical experiments proving the application of this scheme, and we will end on what we propose as our next steps.