  Numerical simulations including magnetic fields have become important in many
fields of astrophysics. Evolution of magnetic fields by the constrained
transport algorithm preserves magnetic divergence to machine precision, and
thus represents one preferred method for the inclusion of magnetic fields in
simulations. We show that constrained transport can be implemented with
volume-centered fields and hyperresistivity on a high-order finite difference
stencil. Additionally, the finite-difference coefficients can be tuned to
enhance high-wavenumber resolution. Similar techniques can be used for the
interpolations required for dealiasing corrections at high wavenumber.
Together, these measures yield an algorithm with a wavenumber resolution that
approaches the theoretical maximum achieved by spectral algorithms. Because
this algorithm uses finite differences instead of fast Fourier transforms, it
runs faster and isn't restricted to periodic boundary conditions. Also, since
the finite differences are spatially local, this algorithm is easily scalable
to thousands of processors. We demonstrate that, for low-Mach-number
turbulence, the results agree well with a high-order, non-constrained-transport
scheme with Poisson divergence cleaning.
