Implementation of a 4th Order-Accurate Finite Volume Scheme in the PLUTO Code

We summarise the implementation of the 4(th)-order accurate finite volume multidimensional scheme for the solution of the classical and relativistic MHD equations, recently added to the PLUTO code for astrophysical plasma dynamics. The method, described in a companion paper (see Berta et al, [2]), employs the constrained transport (CT) formalism to preserve the divergence-free condition of magnetic field and offers some attractive aspects that contribute to improve efficiency and robustness, such as the employment of pointwise reconstructions (rather than one-dimensional finite volume ones); ii) the adoption of upwind constrained-transport (UCT) technique of Mignone and Del Zanna [11] to evaluate the electromotive force (EMF) at zone edges; iii) a fall back approach that increases dissipation in non-smooth flow region through the addition of sophisticated limiting strategies across discontinuities. In addition to the extensive numerical testing already presented earlier, we include here two supplementary benchmarks that focus on the oblique propagation of Alfven waves and the numerical dissipation on a tearing-unstable current sheet. These tests confirm the 4(th) order scheme as a more efficient and advantageous computational tool when compared to the 2(nd)-order methods in describing smooth flows.