Uncertainty propagation by using spectral methods

Riva, Fabio Matteo; Milanese, Lucio; Ricci, Paolo

doi:10.1063/1.4996445

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Journal article

Uncertainty propagation by using spectral methods : a practical application to a two-dimensional turbulence fluid model

Riva, Fabio Matteo ORCID Istituto ricerche solari Aldo e Cele Daccò (IRSOL), Faculty of Informatics, Università della Svizzera italiana Switzerland - Swiss Plasma Center (SPC), École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Milanese, Lucio Plasma Science and Fusion Center, Massachusetts Institute of Technology , Cambridge, USA
Ricci, Paolo Swiss Plasma Center (SPC), École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

2017

Published in:

Physics of Plasmas. - 2017, vol. 24, no. 10, p. 102302

Plasma properties and parameters

English To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173–193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

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