Conservative regularization of ideal hydrodynamics and magnetohydrodynamics

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3339913· OSTI ID:21347182

Thyagaraja, A ^[1]

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1. EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom)

Inviscid, incompressible hydrodynamics and incompressible ideal magnetohydrodynamics (MHD) share many properties such as time-reversal invariance of equations, conservation laws, and certain topological features. In three dimensions, these systems may lead to singular solutions (involving vortex and current sheets). While dissipative (viscoresistive) effects can regularize the equations leading to bounded solutions to the initial-boundary value (Cauchy) problem which presumably exist uniquely, the time-reversal symmetry and associated conservation properties are certainly destroyed. The present work is analogous to (and suggested by) the Korteweg-de Vries regularization of the one-dimensional, nonlinear kinematic wave equation. Thus the regularizations applied to the original equations of hydrodynamics and ideal MHD retain conservation properties and the symmetries of the original equations. Integral invariants which generalize those known for the original systems are shown to imply bounded enstrophy. The regularization developed can also be applied to the corresponding dissipative models (such as the Navier-Stokes equations and the viscoresistive MHD equations) and may imply interesting regularity properties for the solutions of the latter as well. The models developed thus have intrinsic mathematical interest as well as possible applications to large-scale numerical simulations in systems where dissipative effects are extremely small or even absent.

• OSTI ID: 21347182
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 17; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
INVARIANCE PRINCIPLES
KORTEWEG-DE VRIES EQUATION
MAGNETOHYDRODYNAMICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
T INVARIANCE
WAVE EQUATIONS