An Impact of Divergence-Free Magnetic Field Interpolation Using a Solenoidal Gaussian Process Kernel

A new interpolation method using an analytically solenoidal Gaussian Pro-cess (GP) kernel has been introduced within the Unsplit Staggered Mesh (USM)magnetohydrodynamics (MHD) solver, implemented in the University of ChicagoASC FLASH Center’s FLASH4 code. USM computes numerically divergence-free (up to machine accuracy) magnetic fields at the cell interface-centers at eachtime step, and then uses those values to predict the cell-centered magnetic fieldsthrough simple linear interpolation. The GP interpolation method presented here(which replaces the simple linear interpolation) uses the computed cell interface-centered magnetic fields as sample points to train a GP model with an analyticallydivergence-free kernel function, which is used to predict these fields at the cell cen-ters. The performance of the USM scheme using GP interpolation is studied andcompared to the original scheme using arithmetic averaging. Some improvementscan be seen, particularly when calculating the numerical divergence using thecell-centered fields. However, the interpolation is highly sensitive to the hyperpa-rameter l defining the kernel function and its optimization is subject to furtherstudy