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Time-spectral solution of initial-value problems – subdomain approach
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0001-6379-1880
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2012 (English)In: American Journal of Computational Mathematics, ISSN 2161-1211, Vol. 2, no 2, 72-81 p.Article in journal (Refereed) Published
Abstract [en]

Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalized weighted residual method (GWRM), is a generalization of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved. 

Place, publisher, year, edition, pages
Scientific Research Publishing, 2012. Vol. 2, no 2, 72-81 p.
Keyword [en]
initial-value problem, time-spectral, spectral method, subdomains, domain decomposition
National Category
Fusion, Plasma and Space Physics
URN: urn:nbn:se:kth:diva-91443DOI: 10.4236/ajcm.2012.22010OAI: diva2:510276

QC 20121127

Available from: 2012-11-27 Created: 2012-03-15 Last updated: 2013-05-02Bibliographically approved
In thesis
1. Pressure driven instabilities in the reversed-field pinch: numerical and theoretical studies
Open this publication in new window or tab >>Pressure driven instabilities in the reversed-field pinch: numerical and theoretical studies
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated.

Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as  γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3.

A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xi, 56 p.
Trita-EE, ISSN 1653-5146 ; 2013:017
Fusion plasma, thermonuclear, Reversed-field pinch, resistive MHD, resistive g modes, thermal conduction, the boundary value theory
National Category
Fusion, Plasma and Space Physics
urn:nbn:se:kth:diva-121345 (URN)978-91-7501-722-8 (ISBN)
Public defence
2013-05-17, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)

QC 20130503

Available from: 2013-05-02 Created: 2013-04-29 Last updated: 2013-05-02Bibliographically approved

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