A posteriori error estimate in fluid simulations of turbulent edge plasmas for magnetic fusion in tokamak using the data mining iPoPe method

Progressing toward more reliable numerical solutions in the simulation of plasma for magnetic confinement fusion has become a critical issue for the success of the ITER operation. This requires developing rigorous and efficient methods of verification of numerical simulations in any relevant flow regimes of the operation. This paper introduces a new formulation of the Projection on Proper elements method, namely, the independent Projection on Proper elements method to quantify the numerical error by performing a data-driven identification of the mathematical model from the simulation outputs. Based on a statistical postprocessing of the output database, the method provides a measure of the error by estimating the distance between the (numerical) effective and (analytical) theoretical weights of each operator implemented in the mathematical model. The efficiency of the present method is illustrated on turbulent edge plasma simulations based on a drift-reduced Braginskii fluid model in realistic magnetic geometries. The results show the effective order of the numerical method in these multiscale flow regimes as well as the values of the plasma parameters which can be safely simulated with respect to a given discretization. In this sense, the method goes one step further than the Method of Manufactured Solution recently introduced in fusion, and provides an efficient verification procedure of the numerical simulations in any regimes, including turbulent ones that could be generalized to other scientific domains.