We present a novel implementation of a genuinely $4^{\rm th}$-order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) in both ideal and resistive regimes based on the constrained transport (CT) formalism in the PLUTO code.
Our scheme is rooted over the method originally proposed by McCorquodale and Colella but introduces several novel aspects when compared to its predecessors, yielding a more efficient computational tool.
Among the most relevant ones, our scheme exploits pointwise to pointwise reconstructions (rather than one-dimensional finite volume ones).
It employs all the generalized upwind averaging techniques of the upwind constrained-transport (UCT) method of Mignone and Del Zanna to evaluate the electromotive force (EMF) at zone edges, with the addition of a new relativistic UCT-GFORCE average, and ensures robustness through sophisticated limiting strategies that include both a discontinuity detector and an order reduction procedure.
We thoroughly tested such method, producing results that confirm its efficiency compared to traditional low order schemes.