The most effective numerical treatment of turbulence within a transport model of a tokamak plasma is as a multi-scale, multi-physics problem. Multi-scale since the typical time- and space-scales associated with turbulence are usually much smaller than the time- and space-scales of the plasma as a whole, which is the domain of a transport code; multi-physics since a range of possible physics needs to be included in the problem, but these can usually be treated separately.
The work described here reduces the full problem to the coupling of three separate codes: a transport code that evolves the macroscopic one dimensional fields based on geometric information provided by an equilibrium code and transport coefficients derived from running multiple instances of a flux-tube turbulence code; the changing profiles from the transport code are inputs to the equilibrium and turbulence code forming a time loop.
The MUSCLE2[REF1] coupling framework is used to implement this workflow in a tightly coupled, modular and extensible manner, while the unit of exchange between the codes is the appropriate Consistent Physical Object (CPO)[REF2]. The workflow is similar to that described in Falchetto et al.[REF3] and some information about the workflow development can be found in Hoenen et al.[REF4], Luk et al.[REF5] and Luk et al.[REF6].
The EasyVVUQ library developed as part of the VECMA project[REF7] is being used to incorporate the calculation of uncertainty intervals into the workflow. As identified by the VECMA project, different approaches to implementing UQ are possible. The easiest to implement is to treat the application as a black-box and then to apply one of the standard UQ techniques to the inputs and outputs of the black-box. In this case the black-box is the entire workflow run to (quasi) steady-state. This has been implemented with a simpler proxy for the turbulence code in order to make development of the techniques faster.
Work has now started on opening up the workflow so that UQ is applied at the code level within the workflow, and rather than just passing profile between codes, distributions of profiles are passed.
The initial application has been to an ASDEX Upgrade Standard H-mode shot with the density profile taken from the experiment and the electron and ion temperature profiles predicted. The figure on the left shows the measured ion temperature from four AUG standard H-mode shots (with varying heating schemes) and the results of predictive simulations based on a simple model (labelled GEM0) and the results from the workflow using the GEM code at 8 flux-tube positions.
The future challenge will be to bring the pieces of UQ together with the stochastic nature of the turbulence code to examine the feasibility of producing profile predictions incorporating a turbulence code together with uncertainty intervals. If this proves to be feasible with the used gyro-fluid turbulence code, the extension to gyro-kinetic turbulence codes will be an obvious next step.
[REF1] J. Borgdorff, M. Mamonski, B. Bosak, K. Kurowski, M. Ben Belgacem, B. Chopard, D. Groen, P.V. Coveney, A.G. Hoekstra, “Distributed multiscale computing with MUSCLE 2, the Multiscale Coupling Library and Environment”, Journal of Computational Science, 2014, Volume 5, Issue 5, pp.719-731. doi:10.1016/j.jocs.2014.04.004.
[REF2] F. Imbeaux, J.B. Lister, G.T.A. Huysmans, W. Zwingmann, M. Airaj, L. Appel, V. Basiuk, D. Coster, L.-G. Eriksson, B. Guillerminet, D. Kalupin, C. Konz, G. Manduchi, M. Ottaviani, G. Pereverzev, Y. Peysson, O. Sauter, J. Signoret, P. Strand, ITM-TF work programme contributors. “A generic data structure for integrated modelling of tokamak physics and subsystems”, Computer Physics Communications, Elsevier, 2010, 181, pp.987 - 998. doi:10.1016/j.cpc.2010.02.001
[REF3] Falchetto, Gloria L., David Coster, Rui Coelho, B. D. Scott, Lorenzo Figini, Denis Kalupin, Eric Nardon et al. "The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results." Nuclear Fusion 54, no. 4 (2014): 043018.
[REF4] Hoenen, Olivier, Luis Fazendeiro, Bruce D. Scott, Joris Borgdoff, Alfons G. Hoekstra, Pär Strand, and David P. Coster. "Designing and running turbulence transport simulations using a distributed multiscale computing approach." In 40th EPS Conference on Plasma Physics, EPS 2013; Espoo; Finland; 1 July 2013 through 5 July 2013, vol. 2, pp. 1094-1097. 2013.
[REF5] O. O. Luk, Olivier Hoenen, Alberto Bottino, Bruce D. Scott, and D. P. Coster. "ComPat framework for multiscale simulations applied to fusion plasmas." Computer Physics Communications 239 (2019): 126-133.
[REF6] O. O. Luk, O. Hoenen, O. Perks, K. Brabazon, T. Piontek, P. Kopta, B. Bosak, A. Bottino, B. D. Scott, and D. P. Coster. "Application of the extreme scaling computing pattern on multiscale fusion plasma modelling." Philosophical Transactions of the Royal Society A 377, no. 2142 (2019): 20180152.
|Affiliation||Max Planck Institute for Plasma Physics|
|Country or International Organization||Germany|