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Unconditionally stable numerical simulations of a new generalized reduced resistive magnetohydrodynamics model
Author(s) -
Malapaka Shiva Kumar,
Després Bruno,
Sart Rémy
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3847
Subject(s) - magnetohydrodynamics , physics , tokamak , plasma , context (archaeology) , dynamo , resistive touchscreen , tearing , magnetic field , magnetic confinement fusion , mechanics , nuclear physics , quantum mechanics , thermodynamics , computer science , paleontology , computer vision , biology
SUMMARY Reduced‐resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [Finn Bozkaya JM, Guzdar PN. Loss of equilibrium and reconnection in tearing of two dimensional equilibrias. Physics of Fluids B 1993; 5 :2870–2876], modeling plasma confinements in reverse field pinch [Strauss HR. The dynamo effect in fusion plasmas. Physics of Fluids 1985; 28 :2786–2792] and tokamaks [Strauss HR. Reduced MHD in nearly potential magnetic fields. Journal of Plasma Physics 1997; 57 (1):83–87; Freidberg J. Plasma Physics and Fusion Energy . Cambridge University Press: Cambridge, 2008]. In this context, recently, a new generalized reduced‐resistive MHD model, which can make use of an arbitrary density profile was proposed [Després B, Sart R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 2012; 46 (5):1081–1106. EDP Sciences, SMAI, 2012 online 2011]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [Fujita T, Oikawa T, Suzuki T, Ide S, Sakamoto Y, Koide Y, Hatae T, Naito O, Isayama A, Hayashi N, Shirai H. Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT‐60U. Physical Review Letters 2001; 87 (11):245001; Hawkes NC, Stratton BC, Tala T, Challis CD, Conway G, DeAngelis R, Giroud C, Hobirk J, Joffrin E, Lomas P, Lotte P, Mailloux J, Mazon D, Rachlew E, Reyes‐Cortes S, Solano E, Zastrow K‐D. Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive. Physical Review Letters 2001; 87 (11):115001], which was modeled using reduced‐resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well‐posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.