Towards numerical optimization of snowflake topologies

Abstract

In this paper, the framework for gradient‐based optimization of snowflake magnetic divertor topologies is discussed. A continuous in‐parts adjoint approach is adopted to calculate the gradient. A robust grid generator developed within the in‐house DivOpt code enables different topologies in an automated way. However, a large flux expansion exists near second‐order and closely spaced first‐order X‐points. This might induce significant discretization errors. As accurate gradients are needed for the correct functioning of the numerical optimization algorithm, the importance of the discretization error is assessed by calculating the gradient with both finite differences and the continuous adjoint approach on three systematically refined grids. It is shown that sufficiently fine grids are needed to achieve accurate gradient calculation and a corresponding good functioning of the optimization algorithm.