A residual-based compact scheme of optimal order for hyperbolic problems

A new fourth-order dissipative scheme on a compact 3 × 3 stencil is presented for solving 2D hyperbolic problems. It belongs to the family of previously developed residual-based compact schemes and can be considered as optimal since it offers the maximum achievable order of accuracy on the 3 × 3-point stencil. The computation of 2D scalar problems demonstrates the excellent accuracy and efficiency properties offered by this new RBC scheme with respect to existing second- and third-order versions.