Runge Kutta timestepping

The Runge Kutta two-stage timestepping method of Shu¹ at present implements an "extended ghost region" in order to carry out the computation correctly on the second time-integration. However, it is possible to perform this action without an extended ghost region, if one instead time-interpolates surrounding coarse (or neighbor) values.

While the former (present) implemention suffers from the requirement of larger ghost regions on every AMR grid, the latter suffers from intense overhead in parallel computations, as temporal integrations on each subgrid of a given processor would theoretically require communication with grids located on all other processors.

^1. C.-W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 1073-1084.