Abstract
A new fourth-order dissipative scheme on a compact 3 × 3 stencil is presented for solving 2 D 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 2 D scalar problems demonstrates the excellent accuracy and efficiency properties offered by this new RBC scheme with respect to existing second- and third-order versions.
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