High-order implicit solver in conservative formulation for tokamak plasma transport equations
Artikel i vetenskaplig tidskrift, 2025

An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (one temporal and one spatial) featuring stiff non-linearities. The presented numerical scheme aims to minimise computational costs, which are associated with repeated calls of numerically expensive physical models in a processes of time stepping and non-linear convergence within an integrated modelling framework. The spatial discretisation is based on the 4th order accurate Interpolated Differential Operator in Conservative Formulation, the time-stepping method is the 2nd order accurate implicit Runge-Kutta scheme, and an under-relaxed Picard iteration is used for accelerating non-linear convergence. Temporal and spatial accuracies of the scheme allow for coarse grids, and the implicit time-stepping method together with the non-linear convergence approach contributes to robust and fast non-linear convergence. The spatial discretisation method enforces conservation in spatial coordinate up to the machine precision. The numerical scheme demonstrates accurate, stable and fast non-linear convergence in numerical tests using analytical stiff transport model. In particular, the 2nd order accuracy in time stepping significantly improves the overall convergence properties and the accuracy of simulating transient processes in comparison to the 1st order schemes.

Plasma simulation

Tokamak

Diffusion-advection equation

Fusion energy

Stiff non-linearity

Transport

Författare

Andrei Osipov

Chalmers, Rymd-, geo- och miljövetenskap, Astronomi och plasmafysik

United Kingdom Atomic Energy Authority

Dmytro Yadykin

Chalmers, Rymd-, geo- och miljövetenskap, Astronomi och plasmafysik

Pär Strand

Chalmers, Rymd-, geo- och miljövetenskap, Astronomi och plasmafysik

Computer Physics Communications

0010-4655 (ISSN)

Vol. 311 109570

Infrastructure for research and devlopment of fusion reactors: ITER and DEMO

Vetenskapsrådet (VR) (2021-00182), 2022-01-01 -- 2026-12-31.

Ämneskategorier (SSIF 2025)

Beräkningsmatematik

DOI

10.1016/j.cpc.2025.109570

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Senast uppdaterat

2025-03-21