UC Santa Cruz

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 Chicago

ASC FLASH Center’s FLASH4 code. USM computes numerically divergence-

free (up to machine accuracy) magnetic fields at the cell interface-centers at each

time step, and then uses those values to predict the cell-centered magnetic fields

through 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 analytically

divergence-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 and

compared to the original scheme using arithmetic averaging. Some improvements

can be seen, particularly when calculating the numerical divergence using the

cell-centered fields. However, the interpolation is highly sensitive to the hyperpa-

rameter l defining the kernel function and its optimization is subject to further

study.