Naslov
A Meshfree Method versus Analytical Approach to the Solution of the Current Diffusion Equation

Autori
Sesnic, Silvestar ; Poljak, Dragan ; Slak, Jure ; Kosec, Gregor

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
31st Symposium on Fusion Technology, Book of Abstracts / - Zagreb, 2020, 161-161

Skup
31st Symposium on Fusion Technology (SOFT 2020)

Mjesto i datum
Online, 20.09.2020. - 25.09.2020

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Current Diffusion Equation ; Meshfree Method ; Analytical Approach

Sažetak
The paper deals with the comparison of different approaches for the solution of the Current Diffusion Equation (CDE) which governs current diffusion inside a tokamak reactor. The CDE describes the current (or, equivalently, the magnetic field) diffusion through the plasma as a conductive medium and is derived by flux-averaging the Ohm’s law. This transport equation is usually tightly coupled with the equilibrium phenomena (the Grad-Shafranov equation). In this paper, CDE is solved via Meshfree method and an analytical approach, respectively. The Meshfree solution is obtained with a local strong form approach where differential operators are approximated using an augmented Radial basis functions generated finite differences method on scattered nodes. On the other hand, the analytical solution of the CDE is obtained by applying certain approximations to the equation. Namely, time derivative of a flux coordinate at the plasma boundary is neglected and current density driven by non-inductive sources is assumed to be zero. The particular solution of CDE is obtained in a generalized form, where auxiliary functions are transformed into polynomials of arbitrary order in a least-squares sense. The obtained results show the time evolution of the magnetic flux versus normalized flux coordinate. The results obtained via Meshfree method and analytical approach show similar behavior of the magnetic flux with largest discrepancy occurring at the edge of the plasma configuration for the early time period. The trade-off between different approaches is undertaken and the related results clearly demonstrate the validity and usefulness of Meshfree method for accurate numerical modeling of plasma physics phenomena as well as the applicability of analytical approach for benchmarking purposes.

Izvorni jezik
Engleski

Znanstvena područja
Fizika, Elektrotehnika

POVEZANOST RADA