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

Fabio Riva,1, ∗ Lucio Milanese,2 and Paolo Ricci1 1École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland 2Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Abstract 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 [American Journal of Computational Mathematics 02, 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.