Orbital advection with magnetohydrodynamics and vector potential

Orbital advection is a significant bottleneck in disk simulations, and a particularly tricky one when used in connection with magnetohydrodynamics. We have developed an orbital advection algorithm suitable for the induction equation with magnetic potential. The electromotive force is split into advection and shear term, and we find that we do not need an advective gauge as solving the orbital advection implicitly precludes the shear term from canceling the advection term. We prove and demonstrate the third order in time accuracy of the scheme. The algorithm is also suited for non-magnetic problems. Benchmarked results of (hydrodynamical) planet-disk interaction and the of the magnetorotational instability are reproduced. We include detailed descriptions of the construction and selection of stabilizing dissipations (or high frequency filters) needed to generate practical results. The scheme is self-consistent, accurate, and elegant in its simplicity, making it particularly efficiently in straightforward finite-difference methods. As a result of the work, the algorithm is incorporated in the public version of the Pencil Code, where it can be used by the community.