320 research outputs found
Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D
We present an extension of the Karman-Howarth theorem to the Lagrangian
averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws
resulting as a corollary of this theorem are studied in numerical simulations,
as well as the scaling of the longitudinal structure function exponents
indicative of intermittency. Numerical simulations for a magnetic Prandtl
number equal to unity are presented both for freely decaying and for forced two
dimensional MHD turbulence, solving directly the MHD equations, and employing
the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the
third-order structure function with length is observed. The LAMHD-alpha
equations also capture the anomalous scaling of the longitudinal structure
function exponents up to order 8.Comment: 34 pages, 7 figures author institution addresses added magnetic
Prandtl number stated clearl
Improved Accuracy for Fluid Flow Problems Via Enhanced Physics
This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD
Stable computing with an enhanced physics based scheme for the 3d Navier-Stokes equations
We study extensions of an earlier developed energy and helicity
preserving scheme for the 3D Navier-Stokes equations and apply them to a more
general class of problems. The scheme is studied together with stabilizations
of grad-div type in order to mitigate the effect of the Bernoulli pressure
error on the velocity error. We prove stability, convergence, discuss
conservation properties, and present numerical experiments that demonstrate
the advantages of the schem
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