Large Eddy Simulations in Magnetohydrodynamics Flows

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Magnetohydrodynamics describes the behavior of an electrically conducting fluid flow in the presence of magnetic fields. Electrically conducting fluids arise in applications including astrophysics, geophysics, plasma confinement, controlled thermonuclear fusion, liquid-metal cooling of nuclear reactors, electromagnetic casting of metals, ion thrusters for low orbiting satellites, magnetohydrodynamic drive for ships and submarines, microfluidic devices, and molecular biology. The fluid motion of the Earth's core maintains the terrestrial magnetic field, the solar magnetic field generates sunspots and solar flares, and the galactic magnetic field influences the formation of stars from interstellar clouds. These applications require substantially better modeling and simulation capabilities than presently exist. Problems without a clear scale separation, such as turbulence, are still at the frontier of multiscale modeling and simulation. When the fluid is electrically conducting, the turbulent fluid motions are accompanied by magnetic fluctuations. For Magnetohydrodynamic (MHD) turbulence, numerical simulations play a greater role than they play for hydrodynamic turbulence, since laboratory experiments are practically impossible and astrophysical systems (solar-wind turbulence, the most important system of high-Reynolds-number MHD accessible to in situ measurements) are too complex to be comparable with theoretical results. This research project will develop improved computational methods for these important problems. This research project studies mathematically rigorous and computationally efficient methods to analyze direct and inverse problems constrained by MHD models. This includes the numerical analysis of computational algorithms, implicit explicit time-stepping schemes using the Elsasser variables, post processing via time-filters, spatial linear and nonlinear filters, spectral filtering, development of spatial filters specific to MHD turbulence, optimal control, and parameter estimation. Another objective of this project is to investigate the mathematical properties of several models for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows and new numerical models that permit long-time simulations, by time-splitting. The project has a broad impact for training undergraduate and graduate students in analytical and numerical aspects of magnetohydrodynamics, turbulence, and inverse problems.