Examining Alternative Numerical Algorithms for the Accurate and Robust Study of Turbulence

Although it lacks a precise quantitative definition, turbulence is a phenomenon which occurs in many dynamic fluids. A turbulent fluid is characterized by fluctuations across a range of length scales, with energy cascading down from larger to smaller length scales before being dissipated as heat at the smallest length scale. Since turbulence involves spatial and temporal quantities which span many orders of magnitude, it is difficult to model through discretizing the differential equations which govern fluid mechanics. Indeed, conventional discretization schemes such as the wave-propagation method often fail to accurately capture the behavior of turbulent plasmas. As a comparably computationally expensive alternative to the wave-propagation method, we consider the Kinetic-Energy Preserving (KEP) Scheme. To compare the KEP and wave-propagation methods, we examined two-dimensional turbulent systems like the Orszag-Tang vortex. By implementing the KEP scheme for the five moment, two-fluid equations, we obtained a richer, more accurate portrait of turbulent behavior in plasmas.