TVD solves the magnetohydrodynamic (MHD) equations by updating the fluid variables along each direction using the flux-conservative, second-order, total variation diminishing (TVD), upwind scheme of Jin & Xin. The magnetic field is updated separately in two-dimensional advection-constraint steps. The electromotive force (EMF) is computed in the advection step using the TVD scheme, and this same EMF is used immediately in the constraint step in order to preserve ∇˙B=0 without the need to store intermediate fluxes. The code is extended to three dimensions using operator splitting, and Runge-Kutta is used to get second-order accuracy in time. TVD offers high-resolution per grid cell, second-order accuracy in space and time, and enforcement of the ∇˙B=0 constraint to machine precision. Written in Fortran, It has no memory overhead and is fast. It is also available in a fully scalable message-passing parallel MPI implementation.

NIFTy (Numerical Information Field Theory) facilitates the construction of Bayesian field reconstruction algorithms for fields being defined over multidimensional domains. A NIFTy algorithm can be developed for 1D field inference and then be used in 2D or 3D, on the sphere, or on product spaces thereof. NIFTy5 is a complete redesign of the previous framework (ascl:1302.013), and requires only the specification of a probabilistic generative model for all involved fields and the data in order to be able to recover the former from the latter. This is achieved via Metric Gaussian Variational Inference, which also provides posterior samples for all unknown quantities jointly.