Verification and validation procedures with applications to plasma-edge turbulence simulations

Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynamics. Consequently, errors affecting such numerical tools can have far reaching consequences. The present thesis focuses on developing and applying rigorous verification and validation (V&V;) procedures to plasma turbulence simulations, ultimately improving our understanding of the plasma dynamics. First, a rigorous code verification methodology for grid-based simulation codes is presented and used to assess the correct implementation of a physical model in a plasma simulation code. It consists of using the method of manufactured solutions and executing an order-of-accuracy test, assessing the rate of convergence of the numerical solution to the manufactured one. The methodology is then generalized to particle-in-cell (PIC) codes, accounting for numerical schemes intrinsically affected by statistical noise and providing a suitable measure of the distance between continuous, analytical distribution functions, and finite samples of computational particles. The proposed procedure is successfully applied to verify GBS, a simulation code used to study plasma turbulence in the tokamak scrape-off layer (SOL), and to verify a one-dimensional PIC code. Even if the physical model is correctly implemented, simulations are always affected by numerical errors. A rigorous solution verification methodology for estimating the numerical statistical and discretization errors affecting plasma turbulence simulations is discussed in the present thesis. The estimate of the numerical statistical error, such as the one due to the finite number of particles used in PIC simulations, is based on repeating the simulation with different pseudorandom number generator seeds. For the discretization error, the Richardson extrapolation is used to provide an approximation of the exact solution. The solution verification methodology is then applied to quantify the numerical error affecting GBS and PIC simulation results. A further source of uncertainty affecting the results of plasma turbulence simulations is given by the use of input parameters that are not precisely known or accurately measured. A methodology based on a decomposition of the model equation solution in terms of Chebyshev polynomials along the input parameter, time, and spatial coordinates is proposed. This methodology is then successfully employed to investigate the influence of input parameter variations on the results of a two-dimensional drift-reduced Braginskii model. By carrying out a set of validation exercises, the final part of the present thesis is targeted to increase the reliability of our SOL modeling. First, seeded blob simulations carried out considering five different models are validated against measurements taken in the TORPEX basic plasma physics experiment. The comparison of simulations and experimental results sheds light on the dynamics of these structures that lead to large transport in the SOL. Furthermore, GBS simulations are validated against RFX-mod experimental measurements, providing interesting insights on the SOL plasma dynamics in this device. Finally, the impact of the shape of magnetic equilibrium on SOL turbulence is investigated through a rigorous validation of GBS simulations against TCV experimental measurements.

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