Abstract
A comparison is made of two approaches for constructing high-order accurate schemes: one is Directional Non Compact (DNC) and the other is Residual-Based Compact (RBC). Both methods are simple and tuning-parameter free. Real accuracy and computational efficiency are discussed for various 2-D hyperbolic problems including compressible flows with shocks. The DNC and RBC schemes produce high-order results, but the RBC scheme proves to be much better for shock capturing capabilities and computational efficiency.
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